If the trainer or barn manager would NOT allow the owner to be present for the horse’s vet exam, then I would think that the trainer and/or BM are trying to hide something and aren’t to be trusted… It’s one thing if the owner chooses not to be there and lets the trainer or BM do it for them. It’s another if the trainer/BM will not allow the owner to be present.
I have never been in that situation and probably never will be, but if I ever had a trainer or BM tell me I could not be present for my own horse’s vet exam, I’d tell them where to stick it, and then leave with my horse.