Understanding GFCI configuration in basement
The warning from the manufacturer is pretty common on treadmills. the outlets just don't like them. Your right about the downstream outlets being connected to the GFCI by the main panel. I would try plugging your treadmill into that outlet and see if it trips. One solution that has worked for me is to replace the individual GFCI outlet with a standard outlet and replace the breaker with a GFCI breaker in the main panel. Don't ask me why, but it works and I've done it many times. Is your basement finished? Code doesn't require GFCI outlets in a finished basement/room. Good luck