And the coach might have said exactly what you heard and understood. And the coach may think that he IS influencing FA, but I don’t think he is.
All kinds of things are said during recruiting. I think you are right to question whether the school will try to meet the best case, but the only ones who can answer that are in FA. Ask. And then ask again.
This ^^^
Before we applied ED for athletics at a D3 we got a pre-read from the financial aid people. If it was not affordable we were not going to be able to send DD there, but the numbers worked and the actual award was right on their estimate. It wasn’t without some effort and stress: we had to do the entire CSS and FAFSA in pretty short order to meet dates, but once it was in they turned it around on their end pretty quickly as well. Call the FA office and ask.