Well, then I would trust the hotel and not bother posting the question here. You asked for local advice (or so I gathered) and I'm giving it to you. For what its worth, you would have to drive about 25 mph on the freeway for it to take 45 minutes - but perhaps the hotel doesn't want to be liable for complaints if you miss your flight.

Personally, I think you are going to be incredibly early and have a long gate wait. LOOONG security waits (with lines wrapping down the terminal hallway) for security are 20 minutes - and I rarely wait more than 5 minutes. Your longest wait is going to be for check-in.