Here's what the Catechism of the Catholic Church (CCC) has to say on the matter. First, in support of the Scripture verses your uncle mentioned:
CCC 161 - Believing in Jesus Christ and in the One who sent him for our salvation is necessary for obtaining that salvation. "Since "without faith it is impossible to please [God]" and to attain to the fellowship of his sons, therefore without faith no one has ever attained justification, nor will anyone obtain eternal life 'But he who endures to the end.'
And now, the CCC in support of what you've said, Tina:
CCC 846 - "Outside the Church there is no salvation"
How are we to understand this affirmation, often repeated by the Church Fathers? Re-formulated positively, it means that all salvation comes from Christ the Head through the Church which is his Body:
Basing itself on Scripture and Tradition, the Council teaches that the Church, a pilgrim now on earth, is necessary for salvation: the one Christ is the mediator and the way of salvation; he is present to us in his body which is the Church. He himself explicitly asserted the necessity of faith and Baptism, and thereby affirmed at the same time the necessity of the Church which men enter through Baptism as through a door. Hence they could not be saved who, knowing that the Catholic Church was founded as necessary by God through Christ, would refuse either to enter it or to remain in it.
847 This affirmation is not aimed at those who, through no fault of their own, do not know Christ and his Church:
Those who, through no fault of their own, do not know the Gospel of Christ or his Church, but who nevertheless seek God with a sincere heart, and, moved by grace, try in their actions to do his will as they know it through the dictates of their conscience - those too may achieve eternal salvation.
848 "Although in ways known to himself God can lead those who, through no fault of their own, are ignorant of the Gospel, to that faith without which it is impossible to please him, the Church still has the obligation and also the sacred right to evangelize all men."
VI. THE NECESSITY OF BAPTISM
1257 The Lord himself affirms that Baptism is necessary for salvation. He also commands his disciples to proclaim the Gospel to all nations and to baptize them. Baptism is necessary for salvation for those to whom the Gospel has been proclaimed and who have had the possibility of asking for this sacrament. The Church does not know of any means other than Baptism that assures entry into eternal beatitude; this is why she takes care not to neglect the mission she has received from the Lord to see that all who can be baptized are "reborn of water and the Spirit." God has bound salvation to the sacrament of Baptism, but he himself is not bound by his sacraments.
1258 The Church has always held the firm conviction that those who suffer death for the sake of the faith without having received Baptism are baptized by their death for and with Christ. This Baptism of blood, like the desire for Baptism, brings about the fruits of Baptism without being a sacrament.
1259 For catechumens who die before their Baptism, their explicit desire to receive it, together with repentance for their sins, and charity, assures them the salvation that they were not able to receive through the sacrament.
1260 "Since Christ died for all, and since all men are in fact called to one and the same destiny, which is divine, we must hold that the Holy Spirit offers to all the possibility of being made partakers, in a way known to God, of the Paschal mystery.” Every man who is ignorant of the Gospel of Christ and of his Church, but seeks the truth and does the will of God in accordance with his understanding of it, can be saved. It may be supposed that such persons would have desired Baptism explicitly if they had known its necessity.
1261 As regards children who have died without Baptism, the Church can only entrust them to the mercy of God, as she does in her funeral rites for them. Indeed, the great mercy of God who desires that all men should be saved, and Jesus' tenderness toward children which caused him to say: "Let the children come to me, do not hinder them," allow us to hope that there is a way of salvation for children who have died without Baptism. All the more urgent is the Church's call not to prevent little children coming to Christ through the gift of holy Baptism.
In terms of Christian philosophy, I think that one of the most important concepts to understand is a sound philosophy of the human person, namely that every person is created by God with an immortal soul. St. Thomas Aquinas even goes so far as to delineate 3 types of souls:
1) Vegetative Soul: the life force within all living things that is the animating element that we call life.
2) Sensitive Soul: that faculty that gives consciousness the living being to sense its environment and its surroundings and to respond to that environment through the five senses of the body.
3) Rational Soul: this is the soul made in the image of God that is individually created by God and placed into a human being at the moment of conception. This soul is that which allows us to have the Godly attributes of rational thought, creativity, awareness of who we are, awareness of our own mortality, ability to love, to know God, etc.
It is our rational, immortal soul that sets human beings apart from all of the rest of creation, and since God has created us with this eternal soul, he has also given us a way to reach eternal life.
The Church has many canonized saints, but there is not, and never will be, a list of those who are in hell. We simply don't know. And in the words of one modern theologian, Hans Urs von Balthasar, "Dare we hope that all men might be saved?"
Soon-to-be-Blessed Pope John Paul II affirms the reality of hell, but also the hope of salvation for all men. Here’s an excerpt from Avery Cardinal Dulles (seen in full at http://payingattentiontothesky.com/2009/09/28/the-population-of-hell-avery-cardinal-dulles/), who explains John Paul II's position well:
"Pope John Paul II in his Crossing the Threshold of Hope mentions the theory of Balthasar. After putting the question whether a loving God can allow any human being to be condemned to eternal torment, he replies: “And yet the words of Christ are unequivocal. In Matthew’s Gospel he speaks clearly of those who will go to eternal punishment (cf. Matthew 25:46).” As justification for this assessment the Pope puts the rhetorical question: Can God, who is ultimate justice, tolerate terrible crimes and let them go unpunished? Final punishment would seem to be necessary to reestablish the moral equilibrium in the complex history of humanity.
In a General Audience talk of July 28, 1999, the Pope seems to have shifted his position, adopting in effect that of Balthasar. According to the English version of the text he said:
Christian faith teaches that in taking the risk of saying “yes” or “no,” which marks the (human) creature’s freedom, some have already said no. They are the spiritual creatures that rebelled against God’s love and are called demons (cf. Fourth Lateran Council). What happened to them is a warning to us: it is a continuous call to avoid the tragedy which leads to sin and to conform our life to that of Jesus who lived his life with a “yes” to God.
Eternal damnation remains a possibility, but we are not granted, without special divine revelation, the knowledge of whether or which human beings are effectively involved in it. The thought of hell-and even less the improper use of biblical images-must not create anxiety or despair, but is a necessary and healthy reminder of freedom within the proclamation that the risen Jesus has conquered Satan, giving us the Spirit of God who makes us cry “Abba, Father!” (Romans 8:15; Galatians 4:6)"