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Without being at the vehicle when it initially stalled out I can not be 100% certain but it does sound like it ran out of oil. The oil light would not come on if the engine was overfilled, it will come on while driving if it looses oil pressure from an internal problem or lack of oil.
Was the engine making a lot of noise when you limped to the first place after stalling?
The other shop suggesting a new engine also leads me to believe that it did run out of oil especially if it is still not running.
You might want to check with another shop to see if they will inspect it and fill out a report of what the vehicle needs. This will cost you money but if it can be proven the "super store" was at fault I do not see why they would not reimburse you for the inspection also.
Sounds like that are covering up something. If it was overfilled the engine would idle rougher and be smoking. I am thinking they did not have the drain plug tight and it took the 4 days for the oil to leak out or the plug to fall off.
Did you ever notice any oil on the ground after the oil change? Did you actually see the technician drain any oil from your Pilot?