Called and hung up without leaving a message. Out of curiosity, I called back, and got a voicemail that said something like: "You have reached the scam number." Weird.

I've gotten four calls from this number, since April 10. I called it back again today to see if I could discover what it is, and heard this recorded message: "You have reached the phone call that keeps calling and hanging up on people. I believe it's a scam number. Don't call it back." I gather from this that it is some kind of scam call that is spoofing someone else's legitimate Caller ID.

This is a scam.  What happens is, there is some sort of payday loan applied for online, and these people get your information.  They indicate that the loan was made and never paid back.  They have your SSN Address, employer etc.  Lots of people get scared and give a credit card over fear of being arrested.  You cannot be arrested over owing a debt.  Debtors prison went out years ago.  These people pray on the unknowing and because of this get away with it.  unfortunately they bounce all over the country, and because of this, no jurisdiction will take the case.