I'm pretty sure that's not true, but I don't know exactly how Heroku works.

The way I understand it is if no one is making requests to your app they will shut down the dynos, and when you start getting requests they'll spin them back up, up to the number of dynos you're paying for. That's why if your app has been idle for a long time it takes a few seconds for the first request to complete.

This lowers their costs, and presumably the prices for their customers.

I could be wrong though, and perhaps they only turn off dynos for non-paying customers.