I have just never heard of the brake booster causing a "service brakes" warning before, nore from a trailer being connected. I suppose it's not impossible but I had the problem in the past and I dug into it extensively and no where did I find anything pointing to the brake booster. It boiled down to the fluid sensor or stuck prop valve (without a abs light on).I was surprised too and I do not know how they tested the booster to arrive at that issue resolution. Since it only came on (briefly but a couple of times and whenever I trailer) I suspect that the extra weight of the RV on the booster (if it was having issues) would be when the light would come on. However, it seemed to break fine every time.
the brake system has a way of detecting the impedance and knowing if there a issue electrically, like a burnt out bulb or bad ground, bad brake switch, etc but that just results in cruise control not working