Caller ID is just the number.  They leave no message.

I call back (using *67 to block my number).  I hear the following, "<tone> The number you've dialed is not in service. <silence>"  The silence goes on for about 3 minutes and then it hangs up on me.  If this was some phone company message, there would be no extended silence.  I believe the statement plus the silence is their outgoing message.   I tried again later.  This time it rang something like 20 times and then hung up on me.  I'm assuming that this is their message (if it went unanswered it should ring forever).

So they fake a disconnected/unanswered phone and have a spoofed caller ID.  Smells like some kind of SCAM.