Should repair of door jam cause shorts in rear turn light?

That "gunk" you referred to is rust-proofing material and shows the body shop was looking out for your best interest and does quality work. Most shops would spray that in but they typically don't go so far as to tell you about it. They know too many people get confused with too much information and they don't understand that a quality job was performed.

Lighting problems occur all the time, and while I agree it's quite the coincidence it happened after the body repair, that's most likely exactly what it is. You could also say it was caused by the pot hole you ran over, (that's a Wisconsin joke), or you made too many right hand turns, ... After dark, ... In the rain! (That's a mechanic joke). But the point is it is very possible the lighting problem would have occurred anyway regardless of having body work done. There's no way to know for sure until the cause is found and corrected.

If you suspect the cause is related to the body work, the body shop is the place to go back to, not the dealership. If they are not electrical experts, they will be able to recommend a shop with good people. There are lots of independent shops that can handle this type of problem. You do not have to go to the dealer unless that's all there is.

The fact that the system worked at all after you installed a new bulb proves that no wires were damaged during the body repair. If one was, the light would not have worked at all. It's much more common to have a bad socket that is making intermittent contact. You can find that by wiggling the bulb while that circuit is turned on.