The websites in question getting crawled and indexed are generally open and available for anyone to browse. There are parts of the web that are gated off and require authentication and authorization to access. Imagine now that Google found a way to authenticate as you with your bank’s website and index your online banking portal. (It’s not a perfect analogy to what’s happening with Beeper, but I’m just using the one you laid out.)

In a similar way, iMessage as a service requires authentication and authorization to use. It is not open for anyone to use. Beeper is doing something to spoof or otherwise fool Apple into giving the client access. This is the part that’s illegal. And potentially not just “file a lawsuit” illegal but criminally so.

It doesn’t really matter why Apple doesn’t want Beeper or anyone else to use it. The fact that they simply don’t is all that matters.