Well, first of all, there are at least 4 different things we might mean by "salvation". However, to avoid overcomplicating things I will assume you refer to the possibility of living forever with God.
This comes not through any human effort but through the grace of God and the Atonement of Christ - but it is conditional on us doing certain things. One of those things is to receive the proper ordinances (baptism, confirmation to receive the Holy Ghost, etc.) This must be done by one holding the proper authority to act on behalf of God - the priesthood - which is currently only found, on the earth, within the LDS Church. However, these ordinances can be performed by the living, on behalf of the dead, within our temples.
It is also conditional on the person accepting the Atonement - admitting that salvation comes through Christ. This, again, doesn't have to be done in this life, although it helps.
So those who never heard of us, or never joined the church, or maybe didn't even like us at all, can still be saved. But there will come a point in this life or the next when they will have to accept what has been done on their behalf (mostly by Christ, but also in temples). This has been the official Church doctrine pretty much from the beginning, and it makes a lot of sense to me. I don't know of any members who have trouble accepting it.