Switzer's P700 package exists for F10 M5 and package is indeed good for 700 hp and 640 lb-ft. Switzer is a serious company and a simple phone call and vin check with switzer should confirm if the car has P700 package.
I would assume you would do a simple check if you are getting a car over 100k.
I would not call it false advertising just yet. Perhaps owner got P700 on F10 and decided it was not quick enough and maybe they needed P900 GTR package
When you have enough money to buy (not lease, buy) 100k car, $6,995 for P700 package is the least of your worries.