What is the misconception? That paged you linked to says that map tiles are free for use with a few reasonable restrictions:

    Clearly display license attribution, normally in the bottom-right corner of the map.
    Do not actively or passively encourage copyright infringement.
    Recommended: Do not hardcode any URL to tile.openstreetmap.org as doing so will limit your ability to react if the service is disrupted or blocked. In particular, switching should be possible without requiring a software update.
    Recommended: add a link to https://www.openstreetmap.org/fixthemap to allow your users to report and fix problems in our data.
    Recommended: a contact email on your web page or app store page. If we cannot find contact information we will be unable to do anything except block if an issue arises.

Of course, there is no Service Level Agreement:

    Although our map tiles are generally very reliable, their availability to others is on a best effort basis and we offer no SLA or guarantees.

But that seems quite reasonable for donated resources.