The main portion of my 1950's house has a large shed-style roof (the
top edge is the end of the roof...it doesn't slant back down the other
side). I've had a very slowly building leak at the lower corners of
the chimney that is evident inside (the ceiling is cathedral style so
the drywall is right up against the rafters).

I had a guy out today to look at it and he says the drip edge on the
top edge was installed incorrectly. Whereas you want the drip edge
under the shingles at the bottom, he says on my roof they were also
installed under the shingles at the top. That, combined with the
shingles not quite covering the drip edge on that top roof edge is
allowing water to flow under the shingles. Then the chimney pokes
through the felt and that's where the water is coming in. He says
everything looks tight and solid around the chimney itself, which is
what led him to keep looking.

He proposes to install drip edge on top of those shingles and seal it
up, thereby keeping the water from coming in.

Does this make sense? I did some searching around, but couldn't find
anything about the proper way to deal with the top edge of a shed roof.