Come on. Do you really, really believe this happens?
Think about it.
A program graduates a resident/fellow... and then they're going to say, "This douchebag was a piece of crap" when asked for a reference? What would that say about that program? It would say, "We didn't know how to effectively deal with or train this person, so we let them move on despite their deficiencies. Now we're just going to badmouth them."
No. This doesn't, practically, happen. Sure, there may be comments about being a "challenging" and perhaps "provocative" resident and whatnot.
The same should hold true when you are asked about your residency experience. When asked, I've told people the truth: my program was facing some serious administrative challenges, but the core case exposure and training was overall excellent and I felt well-prepared to tackle the most difficult of anesthetics.
If you say ANYTHING other than that, you are potentially shooting yourself in the foot. The program you graduated from is a reflection of your training. If you badmouth it, you are essentially badmouthing yourself.
Be very careful what you say about your program. More so publicly. The Internet isn't as private as you think...
-copro