As daunting as it may seem, it's not impossible to beat these pests. But it takes patience and tolerance for--you said it--letting the phone ring. Many don't make the phone ring off the hook. Four, five times and they give up. From personal experience, I was getting slammed on a daily basis by junk callers. I did exactly what I said starting in 14 and waited when the calls came. I've gone entire weeks without a single call on my landline several times. Seldom do I get more than one a day, and many of the numbers rarely call again. It's a huge improvement from the 10-15 a day I was getting. Of course the scammers (unless it's fake IRS threats) won't leave messages. Outside of finding out your number works, they gain nothing leaving them. Unless you have personal and financial information included in your outgoing message, they can't rip off an answering machine. You lessen 'business' for them by not taking their bait--answering unknown calls. If you're unable to do without the machine, perhaps a call blocker would be a good addition.
Wonderful advice, and by having an answering machine that announces the calling number, makes it unnecessary to even get up, or walk across the room, to look at the caller id.
This group of crooks apparently operates out of St. Peters MO - they are being sought by the authorities, with Life Alert ready to prosecute them in court as soon as they are apprehended.