You're right in that money is not the only motivator for people. I would also argue that if you told them the _real_ reason, aka your own actual motivation behind the offer, the number of people who would actually be "playing" would be much lower.

I would be motivated to collect free data if it meant I was helping save lives, with that help not being behind a paywall.

I would be motivated to play a free game with ads just for the fun of it.

I would not be motivated to play a free game just for the fun of it if my playing of the game was furthering some faceless corporation's profit motives.

In fact, in that last scenario, I would feel tricked, and it would take a non-trivial amount of money for me to not feel that way.