A faulty starter solenoid wouldn’t cause the engine to stall. It might prevent the engine from cranking however when you tried to restart. Cranking is that rrr rrr rrr sound you hear with the key in start. I think the tow driver was just offering up the starter solenoid idea as the reason it wouldn’t crank, not the reason it stalled in the first place.
After a warm engine stalls in most cases it should still crank ok. I think that’s the important clue for this problem. Likely causes are:
- Battery or alternator is failing
- Engine has seized
I’d bet on the first of those, as an engine seizing up is pretty unusual. the first test for the battery alternator is to measure the battery voltage before the first start of the day. Engine unused for 6 or more hours in other words. It should be about 12.6 volts. Immediately after starting the engine it should be 13.5-15.5 volts. Ask you shop to make that measurement and tell us what they say.
BTW, you aren’t alone. My truck stalled in the middle of a busy intersection last summer. I got some passers-by to help push it into a parking lot, which fortuitously happened to be a parking lot for a hardware store. I bought the tools and stuff I needed at the store to effect the diagnosis and repair and was on my way in a couple of hours. In that case the problem was the ignition system.