In our training class there is a fellow with a 3 y/o GSD and a lady with a 1 y/o Terrier (not sure whcih, but it is small). In both cases when another dog goes up to the GSD's owner or the Terrier's owner, they (the dog) gets really testy. When another dog comes up to me, Tal never acts that way. He will come up but I always give him a pet on the head and he doesn't seem to mind another dog getting affection from me. In fact he seems to think the more the merrier.
I figure alot of this is that he has been around other dogs since I brought him home, and he has seen me pet and play with other dogs as well so that is nothing new to him. Are your Labs like Tal too? More curious than anything. BTW, in both cases the owners gave a correction to their dogs.
Mine don't get aggressive - but EVERYONE starts vying for affection!!! It's like, "what about me?" "what about me?"
It's as if they think I'm going to FORGET about all of them just because someone else comes up! They'll push and carry on - and I'll have to tell them all, "NO" and that it's "okay". So they are jealous and spoiled - but not mean about it!