I'm sorry you had a bad experience with FNM, but nothing you stated was "illegal". Only "unnecessary". FNM can make whatever requirements they want. If a customer doesn't want to abide by them, they can shop elsewhere.
When I was shopping for a house, I got my loan approved through a reputable company, but the selling agents firm required that I get another loan approved through a loan office of thier choice. Was this illegal? No. Was it necessary? No. Was it annoying? Heck yes! Still...I could choose to do it or look elsewhere.
If you buy a hamburger from Macdonalds, you can't ask for lean meat.
Your personal knowledge about contract law, psycology or what have you is mute here. They were not doing anything illegal...only annoying.
As for your charge on "bribery"...good luck proving that. Bribery is almost impossible to prove...and most likely, you are only percieving something as bribery when it is not.