The little things sighted as "UFOs" would not be interstellar craft. They would be probes or local runabouts. The interstellar transport might resemble the craft depicted in the film Avatar (which was actually a realistic design), or maybe a hollowed out meteor. The latter would look natural when not executing a major engine burn.
As far as hiding: if they knew they were here to observe an intelligence with conceptual thinking ability and language (even one much less intelligent than they) they would know any overt contact would radically and permanently alter the subjects behavior.
This is all incredibly speculative. I'm just saying that it can't be ruled out by easy superficial arguments. It can't really be ruled out at all. We just don't have enough evidence to rule it in either.
Plenty of wildlife biologists do hide from their subjects when they know their presence will disturb the subjects. Why wouldn't an alien race do the same when observing humans?
Nevertheless you don't even need new physics for this line of speculation. Fusion rockets will do.