If they did so, they would be breaking U.S. law—and it’s one that is being fairly well enforced (the Foreign Corrupt Practices Act, I believe).
Bribing the foreign officials would definitely violate the foreign corrupt practices act. Paying the developer 100k to sever the relationship would not have been a bribe. They may have been outraged by that, but depending on the nature of the relationship that may have been a reasonable fee. It also sounds like it would have been a lot cheaper in the long run.
And what's stopping them from asking for another 100k further down the road again? Paying extortion money is ALWAYS a raw deal. Your argument is illogical.
Bribing someone is a crime, and not something you want to admit on a website. I think there are U.S. laws that also forbid U.S. companies from bribing foreign officials.