I've had an Epson Workforce 630 All-in-one printer for a couple years now.
If someone is on the phone, I can't print. The printer's screen reads an error message that the phone is off the hook, with two choices at the bottom indicating send or receive. I have faxed on this machine minimally but I don't think I've tried to receive before. I've had trouble getting the fax functions to work.
I've looked through the manual and googled. It's hooked up like the manual says. And I do have a DSL filter on the line.
That is relatively common behavior for multi-function devices. You might consider disconnecting the phone line from the Epson except when you want to send or receive faxes.
If we knew what it was we were doing, it wouldn't be called research, would it?