Wow, touchy subject. I am also with Syth on the subject of spanking.
I was spanked and I didn't learn anything more than to fear ticking off my parents. It only served to teach me to not get caught.
On the original topic, I have been in a similar situation and my response was to let the other adult know very clearly that my child's behaviour is not their responsibility. Period. End of discussion. If the child misbehaves, tell me or my wife and we will deal with it appropriately. It is our child and we know what is appropriate for that child.
Being in the military for quite a few years, I have seen the gradual disappearance of "corporal punishment" in training establishments. When I first got in, and I am sure there are many on this forum who will agree, physical punishment was common but we have evolved as a society. There are far better ways to deal with disciplinary issues than simple "fear of consequence"
my 2 cents......take it or leave it.