I have only ever had the game crash from the trainer in scenarios where I have tried using the wrong trainer. I.e. the trainer version didn't match the game version. I think maybe some people download the steam trainer when they should be using the retail trainer, or vice versa.
If you are positive the trainer version and game version are the same, then try reinstalling the game 1.01 patch or 1.02 patch, whichever you use. Sometimes the patch doesn't install correctly which would cause the higher version trainer not to work.
No there is definitely a problem with the trainer as far as I can tell, no matter what you do the game will crash. There are instances where I can load the game and have the game running for a short while and then all of a sudden, the game just freezes and crashes on me.