If anyone is keeping time in local time rather than Zulu/GMT/UTC , they are doing themselves a disservice !
If you work DX or anything else, logs should be kept in Zulu/GMT/UTC which should all be pretty much the same. If you use LoTW, Eqsl or any other QSL service, you may not get all you confirmations/QSLs because of time discrepincies .
As a QSL manager many, many years ago, I handled around 25,000 QSL requests each year. This was in the days before online logs and everything was done by checking paper cards against the DX station's logbooks. I bent over backwards trying to confirm each QSO, but times were so screwed up that many hundreds of cards went in the garbage unconfirmed. This was not the DX stations fault, but rather that of uninformed operators.
Things are so much easier today with online logs like LoTW, Eqsl, etc. that only excuses are 1) you never worked him, 2) your call was copied incorrectly (a.k.a. BUSTED) or 3) poor record keeping by requestor.
This is mostly for newer operators who may not be aware of proper procedures. You "old timers" should already know all this. Yes, I made a few mistakes when I started out many long years ago.
Hope this clears up any confusion.
73, Jerry n9avy