I'm going to go against the flow here.
The most likely scenario, in my opinion, is that the doe was babysitting. We see that frequently here, most recently just last weekend. One of our 'resident' does came into the yard with 3 fawns, which were running, bucking, and chasing each other around. They camped in the yard for about an hour, then down the hill comes another doe. One of the fawns ran up to her and they left together. Here they are:

A couple of times over the years I have seen definite sets of triplets, but never a litter of 4.
~Picture doesn't seem to be working at the moment; will try a fix later.