My answer is not meant to be final nor definitive and I am not really experienced with dogs, not at all, but I feel like I could help with some insight. I definitely want to attempt expanding it if you could provide additional details.
It's a bit difficult to guess accurately whether your dog's trainer is right or wrong with their diagnosis as of the reason for nibbling. But generally their suggestion of discouraging this behavior is in my opinion correct and I could emphasise with it, because such nibbling could be seen as somewhat a sign of the puppy having a bit of bad manners - or, depending on how hard and intrusive does he nibble, maybe not even that bad - but nonetheless a bit crude and unrefined. I could see how that could be seen as undesirable, even if it's devoid of malicious intentions and not challenging your dominance - but anyway they got concerned this behavior could be susceptible to being misinterpreted by puppy's playmates (either dogs or people) and escalate to aggression or just a general distaste towards him.
It's natural and common for puppies to be chewy and mouthy and it's their way of interacting with the world but I guess your dog's trainer has got somewhat alarmed about the potential antisocial outcomes of continuing to allow your dog's behavior, even if they didn't get the exact reason right.
But nonetheless - yes, I could as well believe your puppy's behavior to be just a form of reciprocal grooming and it would make sense to me. I've recently read a really wise explaination on this site, I can't recall the author right now, but in essence they said that the mouth is what puppy has the closest to having a hand, so that's exactly how it could interact with the environment.
I asked in the comments about teething because that would additionally encourage chewing-related behaviors. But puppies are chewy anyway, teething or not, and as I am thinking longer about it I think it wouldn't be the sole explaination even if the puppy wasn't to have had his teething finished months ago, because as you clearly mentioned his behavior is in response to your grooming/petting - and teething would in contrast cause constant agitation and discomfort in that context, leading to overall increased chewiness and mouthiness unrelated to a single stimulus like grooming.
And I asked about the breed just to google out of curiosity and check whether the breeds are known for some behavioral quirks that could give me some clue, but there weren't any to be found.
In conclusion if I were you I'd generally trust the professional if they adviced me to discourage this behavior.