I really don't know. I have never even heard of this before now. The trainer says he checked somehow and that was how he knew for sure, but what made him speculate was when Dakota tried to mount a mare through the fence. I just know that it was most likely not a vet who did the procedure.
I'm just getting bad vibes about this trainer, I feel he's using the horse's supposed behaviour to excuse why he hasn't made the expected progress with him. Get a vet to run a test (they'll probably have to send the sample away), observe his behaviour at home and if you know any experienced horse people, get them to give you a second opinion on his overall behaviour and if possible have them expose him (safely!!) to a mare in heat to see his reaction.
And, my boy is a studly fellow but so long as you have his respect he'll refrain from getting excited around the mares while being worked with, and will walk past other males that are challenging him without so much as a glance - your horse doesn't sound crazy or unruly within your experience, so if the trainer is having trouble your horse may not think much of him.
Just my $0.02