It is a fact. Not only did (I think he's retired now) he speak during the course of instruction, he was actually part of the training.He was hired on to work with SERE training at NASNI or so the interweb "facts" say...
His SRO was then CAPT Stockdale, who actually ordered him to leave early despite his protests.
As far as I am aware VADM Stockdale remained involved with west coast SERE for many, many years. In fact, he had a reserved parking spot at the FASO bldg. Given VADM Stockdale's close association with the program and Doug Hegdhal's participation in the training, I think we can accept what he says as the truth (although I don't think anyone was doubting his POW stories).
Besides, does it really matter how he ended up in the water? He was instrumental in delivering an accurate picture of the status of several hundred downed aircrew being held in Hanoi.