I could get into theological rewordings about how "the Son of Man came not to be served but to serve." (Mark 10:45). But yes, I would basically concur with your explanations.
Not to mention that many people seem to miss the purpose of eternal life as taught in the Bible. Everyone here seems to assume that the ultimate reward of eternal life is to be reunited to one's family and friends. But as my pastor back in college used to ask, "would you want to be in heaven if Christ were not there?" The answer must ultimately be no, lest one desire salvation for all the wrong reasons (and therefore not receive it). The first question in the Westminster Confession essentially addresses the meaning of life: "what is the chief end of man?" The answer is, "the chief end of man is to glorify God and enjoy him forever." The purpose of salvation according to the Bible is to enjoy God. Not reunion with lost family, not streets of paved gold, and not any material comfort, but God himself. As you alluded, most churches in America teach a watered-down Christianity in which people of all religions are going to heaven and in which it's OK to worship God however you please (or not at all). The Bible neither teaches that people can be saved while practicing whatever religion they wish, nor that God requires nothing of man. It seems to me that a view of God has been promulgated in America in which people can invent facts about God and call it doctrine. I don't mean to lay any blame on the posters here who espouse such beliefs. On the contrary, it's the church's fault for preaching man-made religion. Even we physicists seem to have forgotten that just because something makes sense or is intellectually attractive doesn't make it true (anyone remember the ether-based explanation for the presence of magnetic dipole moments in electrons?). If one is to accept what the Bible teaches about the divine, then we must understand that the end goal of all things is not us, but God.