I saw this question a couple of weeks ago and was interested in it, I have just got back from spending 2 nights at the Tour de France where I happened to stay in the same hotel as one of the teams. So I asked one of them.
I'm afraid it has absolutely nothing to do with protection, or with ventilation. In fact you hit upon the disadvantage of a skinsuit in your question - they do not have pockets. Not having gels/food becomes important in a 4-5 hour race.
In fact, even despite this disadvantage, you will on occasion see riders (normally specialist sprinters) wearing skinsuits in a stage, especially one where there the finish is expected to be a bunch sprint. Under such circumstances it becomes the responsibility of a poor old domestique to carry food and gels on behalf of the sprinter. (Heck, I even saw a spectator wearing one!)
So I would guess that the risk mentioned by the commentator is just that the domestique isn't close enough to the sprinter when they need nutrition.