I'm no expert, but I have studied dog behavior recently. Here's my theory:
When a dog lies on its back when meeting another dog, it displays passive submission--the most submissive message a dog can give another dog. As an owner, its a comfort to know that the dog is not going to be a risk for attacking other dogs. It feels comfortable being at the bottom of the pack.
Unfortunately, dogs understand this pecking order, as well. To a confident dog, meeting a submissive dog is a non-challenging, ego-reassuring experience. They go up, sniff the submissive dog, and then ignore it. Such a lowly dog is of little consequence.
The problem probably arises when the low-man meets another low-man or a dog that lacks confidence. The unstable dog gains rank by dominating the submissive dog, who passively welcomes being outranked. Standing over a belly-up submissive dog is a sign of dominance. When the submissive dog is called away/removed before the dominating dog approves, the dominating dog feels its authority is challenged, resulting in sudden aggression.
I'd definitely talk with your trainer and continue socializing your dog. In my opinion, your dog is doing everything fine, but you want to be sure that your dog remains confident even if it stays submissive (which it probably will). You dont want your dog to become fearful with negative dog-on-dog interactions.
If you find yourself in another situation when you see another dog asserting status over your dog --such as standing over it-- before moving on, ask the other dog owner to call their dog away first. This way, the dominant dog will "release" your dog, and you will hopefully reduce the other dog feeling challenged.
Cedar (tri), Willow (blen), & Holly (ruby)