The FBO manages several private jets for owners, but yes they also do some 135 work as well. The aircraft in question was not part of the 135 operation. The owner just didn't know the rules.
As to the ORIGINAL question, I see nothing illegal about the operation. It would be legal as a commercial pilot, and if the CFI is providing instruction as well, doesn't matter. I myself have gone with a student pilot on a cross-country that was tied to a business meeting. It was a two birds one stone type of thing, he got a lesson in while turning a business trip into a shorter affair.