It's not clear if the 'they' in your statement is referring to OSM or a hypothetical non-profit, but, if OSM, they've always done this, I believe.
There are plenty of big users of OSM based tiles that would easily take down the OSM servers, so they have to either host their own or use some third-party to do so (MapQuest is surprisingly popular here, since they have capacity to spare and they'll serve OSM tiles up to some limit before starting to charge).
"OpenStreetMap data is free for everyone to use. Our tile servers are not."
If you are a commercial provider, you can expected to be held to tight standards regarding your definitions. A not-for profit gets a lot more leeway, and "heavy use" is about as specific as OSM needs to get. If you are wondering whether you are crossing the line from "reasonable" to "heavy" use, just assume you've crossed it and make an effort to move your traffic onto your own tile server.
There are plenty of big users of OSM based tiles that would easily take down the OSM servers, so they have to either host their own or use some third-party to do so (MapQuest is surprisingly popular here, since they have capacity to spare and they'll serve OSM tiles up to some limit before starting to charge).
"OpenStreetMap data is free for everyone to use. Our tile servers are not."
http://wiki.openstreetmap.org/wiki/Tile_usage_policy