There really is no link between being permitted to lick plates in some contexts, to stealing food from picnickers.
Dogs are very context specific learners... if you teach your dog he can lick plates in the dishwasher but not when they are on the floor, or table, thats what your dog will do.. therefore a plate on a blanket on the grass is likely to remain unlicked.
One of mine must polish every plate, however she would not TOUCH a plate that still has food on it.. the context is wrong.
Another of mine would not lower himself to lick a plate ever, it is not worth his effort. However if he was off lead and came across a surprised picnicker, he absolutely would have it away on his toes with a sausage roll or scotch egg, he is an excellent opportunistic thief (and as a result is not offlead anywhere one might find picnics!)
This context specific learning is also why its very hard to teach dogs NOT to raid picnics. We teach them not to take food from our plates as we sit on the sofa, or at the table, inside our homes or occasionally, in our gardens. Thats a very limited context.
Food in a tupperware box, on the ground, in the field or park a dog associates with walks is a TOTALLY different context, and likely one most people have not trained their dog with specifically, and so the opportunistic scavenger, which is what a dog is (not a hunter, a scavenger!) is highly likely to take that opportunity.
I work very hard on teaching my dogs not to take food from the ground outdoors, but for most dogs you'd need to teach a behaviour in multiple locations, levels of distraction, variety of context, before the dog will generalise that behaviour to apply 'everywhere' and it is always far harder to teach a 'don't do this' than a 'do do THIS'.