Assembly is one example of manufacture, so that distinction isn't really the one you think it is. Output is tracked by value added, so the mythical "car comes missing a single bolt which gets added in Flint" doesn't really show up in the output numbers, if that's your worry.

Do you think that's a reasonable way to measure abd report manufacturing output?

Is laying our heads at the GDP idol's feet a reasonable measure of what these activities contribute to national welfare?

GDP is a pretty good measure of national incomes and, yes, I think income is a good number to look at if you're judging welfare.