I am completely baffled by this, and alarmed (not doubting you). Where in $$$ is the logic in requiring UK address to drive in UK? And why might it be the business of Hertz, etc, to prove where you live? DVLC does not require that proof!
If they asked it for the credit card, I might regard it as pertinent, but can anyone explain the DL bit? I have a UK licence, no UK proof of address (thankfully) and no problems using it anywhere - yet.