If a stranger came up to me and asked if he could tickle my children, I would tell him no and then probably go to another area of the park. While his intentions may be harmless, you just never know these days. I most likely wouldn't report him or call police though, unless he actually did something that was inappropriate.
I would be kind of creeped out if someone came over and asked me if my kids can tickle him. I don't know how I would react, but I'd probably be shocked at first that he's actually asking me this. I would think to myself, if he's being serious.
It seems as if he thinks that by asking permission, it makes it ok for him to be tickling children that have nothing to do with him. I can understand the pleasure he gets in bringing joy to a child but if he has his own family members that he can do it to (which that article states that he does) I don't see why he should feel the need to go to parks looking for children to tickle.