What did you find was loose in the end? That's honestly terrifying and my biggest fear with electrical work. I've used those push ins a few times myself for convenience. Your story is making me go check every single one in my house this weekend. A little extra time with wire nuts sounds way better than risking a fire.
Totally get that urge to check every single one after reading this. It reminds me of how many "time-saving" products are actually just passing the risk onto us later. Like quick-dry spackle that cracks in a year or those furniture straps everyone ignores until a shelf falls. We trade a lot of safety for a little bit of speed.