Believe it or not, it was because in the park there was a playground used by kids. Paranoid Parents called 911 and reported it.
So, he was actually arrested and taken to jail for sitting in his car eating lunch and reading a book? What was he charged with?
Why does this make it unlikely? Assuming he’s a properly licensed PI and has a reasonable legal excuse, why would the cops care?
In fact, I’d think that him still being there after the cops talked with him makes it more likely that it’s a PI. Not saying that’s the most likely explanation, only that I don’t think you can rule it out just because the cops talked to him.
Of course, if the OP really wants to know, why doesn’t he call the cops and ask? They did talk to the driver and were evidently satisfied with whatever explanation they got.