see https://en.wikipedia.org/wiki/The_Open_Source_Definition for what qualifies as "Open Source"
OSI approved open source that is. And you can tell users anything you want actually. What you can't do with OSI approved open source license is choose a license not approved by OSI, doesn't matter what it says.
But OSI approved open source is not true descriptive open source. SQLite, for example, is universally recognized open source, but not OSI approved. You can go this road and use a descriptive term and ignore OSI and its corporate backing.
So, yes, you can have an open source license that isn't OSI approved. However, leaving aside a few edge cases like public domain, there's pretty wide acceptance of OSI licenses as the population of significant open source licenses.
[ADDED:In practice, the FSF's list of free software licenses and the OSI approved license list line up pretty closely--with the exception of PD+source. If someone wants to argue that the FSF's list is the one we should go by, I'm not really going to argue.]
I do think it is potentially appropriate to have thoughtful discussion over whether the current open source definition is too narrow but I also think it is useful to have a generally agreed-on definition.
