Wouldn't going home have solved their problem?

It's been a while since I've seen this movie, so bear with me if my recollection of the film is a little hazy. If I'm not mistaken, the whole basis of the plot is that Ecks believes his wife is dead and vice versa (the wife also not knowing her own death was faked), both thinking the other died in a car explosion each witnessed at the exact same time.

So wouldn't, I don't know, going home just solve this problem? They'd go back and simply see his or her respective spouse is actually still alive. For that matter, wouldn't their friends and family have found something suspicious about going to two funerals, especially seeing Ecks attend his wife's funeral after they've all just attended his (or vice versa). This whole plot thread just gets a chuckle out of me whenever I think of it.