Have I ever declined someone after approving/offering them the house? No. However...
I do not hold with the "first person that applied and is qualified is my tenant". I process everyone who wants to apply for the house. Then I verify employment, credit, background and current and past residences. Then I score everyone in 6 areas. Whoever gets the highest points could be offered the home. As long as I apply the same scoring to each applicant there is no cause for concern about discrimination. If during the process I find that something doesn't add up with their story, job, history, cleanliness, attitude etc. I can find a reason to deny their approval. And it has NOTHING to do with the protective classes and everything to do with them not filling out the application completely, or omitting a previous address, or not getting back to me with responses in a timely manner, etc. All these things can be used to deny an applicant if you get "negative energy" from them and think they will be a pain in the backside.
If I go through all of this including several phone calls about why they want to move and general chit chat and decide to approve them... and then on the final walk through they show their true colors of being nut job? It would take a person stronger than me to stop dead in my tracks and say... I'm sorry, I don't think this will be a good fit after all. Have a nice day. But it could be done I suppose. Would love to hear others thoughts on how to not let this happen.