So, not that I didn't believe either side... so I decided to try it... my car is out in the driveway at 22f, inside is 32f, and I plugged it into the UMC on a 120V outlet(Ironically a few feet from my HPWC!) about 15 minutes ago... I had intentionally left the car sit and get its battery cold(3 hours in the 34f garage, another hour outside) before starting to charge. The tesla app says it'll be done charging in 5 minutes(!), and is taking 5amps at 118V to add 0 miles/hr to the battery. I realize 15 minutes isn't exactly a scientific test, so I'll leave it going until morning and see if it has added anything at all to the battery in the next 9 hours or so. I'm not really expecting much other a slightly increased electric bill.
While I watched, it flashed to 1mi/hr for a second or two... cooking with gas....err...electrons. Its now happened TWICE, so assuming its 2 seconds per minute, I'm getting 3 feet per minute....(5280 per hour divided by 60 minutes in an hour, divided by 30(units of 2 seconds per minute))
I've turned off the apps and stuff so it can sleep. I might check it again in an hour.