"To the unintiatied, it all sounds like a joke, as, frankly, does much of Catholicism in the U.S. today."
I'm a Bible based Christian and there is NO allowance for an "annulment" but divorce is permitted under certain situations. An "annulment" is not Biblical.
It's about as Biblical as it possibly could be. In fact, in the Gospel of Matthew, Christ specifically recognizes the case where a marriage may appear to exist but not exist in truth when he says that divorce is prohibited "except for porneia". "Porneia" means, not adultery ("adultery" in Greek is "moicheia"), but unchastity; an irregular or unlawful marriage arrangement, de facto "shacking up".
The term "annullment" is not really correct anyway. The correct term is a "Decree of Nullity"; a formal finding that no real Christian marriage ever existed (though a marriage did exist in civil law).