And are those kids’ parents in the grocery line too?
See, that’s the thing: when you are in a school environment, or coaching, or working with the Scouts, etc., you are there with the explicit or implicit permission of the parents. When you are talking to random kids in the grocery line, Mom or Dad is most likely right there, and can monitor your interaction.
When you are seeking out random kids on the playground, out of direct contact with the parents, then there is at least the possibility that you are testing boundaries: which kids are vulnerable? which ones are trusting? which ones can you groom until they feel safe enough to come somewhere more private than the open playground, and then will keep quiet about that “special game”?
If several parents, watching this guy over a period of time, can’t figure out that he’s got a kid with him, then that raises the possibility that he’s not at the playground to interact with his own child. So why is he there?
Asking him which kid was his might have allayed suspicions, but maybe even then it should not have, because as others note, the fact that he has a child himself doesn’t mean he can’t be a pedophile. If he is behaving oddly, then he might be socially awkward or he might be a real threat. How do you tell?
As for paranoia, there are around 1200-1400 law-enforcement-related homicides a year, but that covers everything from the most egregious abuses to the attacker killed at Ohio State yesterday. Meanwhile, something like 60,000 child sex abuse cases are prosecuted each year (which of course doesn’t count cases where prosecution is declined or the abuse never even reported).
Finally, suppose the OP had asked the question and received an answer. Then what? If the guy says he’s there with his child, should OP immediately assume, “oh, everything’s ok”? What if he says he’s not there with his kid?