I eat cold pizza a lot. I don't see the worry. Mine even has meat but no cheese. Ive had it almost once a week this whole pregnancy. The meat was cooked once then out in the fridge. How is that unsafe to eat? Unless you have a gross fridge lol jk
The bacteria that can cause food poisoning are everywhere, you don't have to poke at a piece of food with a dirty finger to get them in there. In the time period when food is cooling/lukewarm, that's an ideal time for bugs to breed. Refrigeration can halt/slow that growth, but it doesn't kill the bugs.
So if you ate your pizza while the rest of it sat on the bench, it could well have bacteria in it. If you don't reheat it to kill the germs, you're at risk of food poisoning.
It's not terrifically common, but it does happen, and that's why the recommendation is there.