It's one thing to be a boy scout, but it's another entirely to get accused of severe, frivolous charges while abroad, or to drive up to an armed cartel/militant roadblock, and then say "I'm sorry, bribes are against corporate policy and illegal in my country" when asked for $50.
Shame on any company for creating a clause like that and risking their employees lives instead of just remaining silent on the matter. Make no mistake, bribery isn't optional in many parts of the world, it's a robbery by a uniformed official.
A bribe needed to get a lucrative contract for your company: not ok.
Paying off a local cop so he won't throw you in jail for no reason: totally ok.
The US is concerned with preventing the former, not the latter. I would be surprised if any US company is advocating people pay the first kind of bribe, at least publicly, as that's quite illegal in the US (I'm sure it happens, but as quietly as possible). But I would not be surprised if US companies tell employees to pay the second kind of bribe, as well they should.
Courtside tickets to an NBA game? Not okay.
"Your vehicle does not have the permits. You need to come with me" at gunpoint in sub-Saharan Africa? That's a matter of life and death, potentially.
There's little difference between bribes and highway banditry in some places, and not playing along will very likely not end well for you.
Recourse in cases of abuses of power is already hit-and-miss in so-called "civilized" countries. I wouldn't count on it in countries that can't even agree on who's in charge somewhere.