What many of these real estate investors do is have a phone number on their bandit signs or use in their robodialer voice mails that forwards to the answering service. That phone number might be provided by services like callfire or callrail where you can generate lists of numbers. Some services let you script all actions.
Callfire allows for things like enabling recording on the call forward (potentially illegal) when someone calls it. Then investor themselves or pays a virtual assistant like $3hr to sift through all those calls for any potential leads. You can hear the entire call to patlive if you wanted to. Or they just trust patlive to forward messages as they’re the answering service.
So long as your answering service or where you’re generating your numbers doesn’t blow your cover then you can keep this game up for a long time. That’s what these answering services are trained to do is protect their clients identities. But I doubt that holds up when the FTC comes knocking.