We'll see what they say but now that everything was back to "normal" pre and post tow, I don't have much confidence in dealership diagnostics. I have also never been in a vehicle that had as wonky as a response to a partially failing battery, if that is really the case.
Throughout my lifetime, if a battery was weak, you'd know about it and wouldn't be able to start the vehicle. Not be able to start the vehicle but not shift in to a gear of motion!
It has also not been all that cold, yet, but was colder a few weeks ago when I bought the vehicle. I would have expected a questionable battery to show it's ugly face in temperature extremes. Last evening it was above freezing I believe.
If you haven't already, be sure to check out the video. It's "hidden" so only people with the link can view it, as it's not publicly visible on youtube.