The doctor has to sign a form saying that you had your physical. Paperwork confirming the colonoscopy or breast cancer screening.
Her employer holds monthly health challenges and classes - so they can track who participated in many of those via a roll at the class.
But there are also a number of things, like exercise or increasing veggie intake, that are self-reported. I'm not sure anyone can get to the requisite points doing just the self-reported stuff. And they do have a very ominous sounding statement about certifying that you aren't lying about doing the things you said you did.