Well, exactly! This can be a problem if incest is a regular occurrence, generation after generation, within the same confined gene pool - and depending on the number and kind of flawed recessive genes present in the first place. Where this is most likely to happen is in a a small, geographically isolated community. It doesn't matter what moral taboos the rest of the world makes, these people have no choice: they can marry one another or nobody at all.
There is no biological obstacle to them mating and producing children. Nature doesn't care. If a genetic combination doesn't work, Nature kills it off and keeps on truckin'. If the incestuous clan is lucky, the fatal defects will be bred out in a few generations; if it's unlucky, it will grow weaker, less fecund and eventually extinct.
Inbreeding is not an instant and inevitable problem in one isolated case of a brother and sister being raised apart, meeting as adults and falling in love - unless they both carry a fatal recessive gene. This doesn't happen every Thursday, and their children - unless the busybody, who thinks its his calling to ruin their lives, takes the children away to be raised by different anonymous foster parents - are even less likely to marry each other, because the familiarity non-attraction principle applies if they're raised together. So, what's the probability of this one meeting even taking place, let alone causing harm down the line? (Ick factor aside, realistically.)
No matter how much society disapproves of incest, no matter how seriously the law takes it, Nature doesn't care; biology doesn't care; the animal body doesn't care - it keeps happening. Unfortunately, the kind of incest that happens most often is perpetrated on the young and vulnerable by someone older and stronger. It's not the consanguinity that makes it wrong, but the assault.