When asking yourself such questions, ask what law(s) might be broken. There are plenty I’m sure, but your PI should know exactly how to stay out of trouble. Unless when, maybe later, it comes out that he was up to shenanigans…
And no, I’m certain no justification is required to contract a PI. Imagine if there was, no one would do the job.
Funny seeing the line in Oklahoma. I’m from Tulsa and have always said Coke, but it wasn’t odd to hear pop. Soda? Get. Out.