I thought the main risk was if the battery was pierced, ike getting wedged in a seat and people recline and it damaged the battery structure.

They tell you if you drop your phone between seats, to call a flight attendant to help you, presumably because there's a greater risk of the phone and especially the battery being damaged, causing a thermal runaway.

But simply connecting the battery bank to a device could cause it?

I've never had devices or battery banks get hot. However, on wireless batteries, my iPhone does get very warm. Not so hot the I can't touch it but noticeably warm.