Vets are not breed experts.
If you've been sold a cat as pedigree and have pedigree paperwork for it and you have reason to believe cat is NOT pedigree, the only way to check is to get DNA tests to show it is the offspring of the parents listed/of parents that are registered as that pedigree.
If you bought the cat without paperwork or the breeder will not provide DNA evidence... your next best bet is to show cat to a pedigree judge of that breed (probably several) and if they agree cat is pedigree it probably is, if they think it isn't it probably isnt... but this is less likely to stand up in small claims court.
As for the neutering - some cats are both, its not uncommon that a cat is both male and female and this is not determined until the vet opens the cat up and finds things are not quite as expected inside.
I am not quite sure where you are counting three operations for - microchipping is not an operation, its a needle to the scruff.
Your vet will have opened the cat up for a spay, and discovered testicles, removed those and gone looking for ovaries just in case - did you want her to not do that? That might have left your cat fertile or at least, able to come into season and call even if not actually reproduce.
Or did you want her to leave the testicles and let your cat risk cancer (internal testicles are a much higher testicular cancer risk) or going around spraying and mating?