As long as the drip edge of the next course covers the previous nails, you are OK. I would agree that they should have been up higher, but that is done. I also hate comp shingles fastened to a roof with power tools and especially staples, but that is too late.
I think that he is taking advantage of you. I would not do a thing.
This sounds like the "magic bullet" theory, I cannot imagine water rolling off the shingle, then turning 180 and going up and under that tap and then finding that rusty nail and then driping along that barb.