I had a plumber over to install a water heater. Even with his acetylene
torch, he had trouble disassembling the joint, but finally succeeded.
He shortened the pipe 3/16" so there was perfect alignment with the
union on top of the faucet. Tightened it, and guess what: there was
still the same tiny dripping. So my theory about misalignment being the
problem turned out to be wrong.
He retightened it as much as he dared, but the leak persisted. He solved
the problem by applying pipe dope around the leaky threads.
Thanks to all for you informative comments.