You may be struggling to find a AIO for the home that can do this. The paperless office goes a bit against the printer vendor manta. The machines sell so cheaply that they want you to print everything you receive so you use more ink/toner to make more money 😉
The reception of the received fax into the Mac will depend on the software included for the device. I've seen this function in the SOHO market for Windows but the Mac always seemed to have missed out on this feature with the low-end devices.
At least there are now more devices that can fax from the Mac. This wasn't the case a few years ago. The Canon MF series has a fax driver that will allow "PC-faxing". But it certainly cannot receive the fax back into the Mac. This sort of thing is available for office MFD's, where they can re-direct incoming faxes to email or a shared network folder. But you need to spend a considerable amount to get this.
I was going to suggest you check out Brother, as they have a good reputation for having Mac software equivalent to what they offer for Windows. But then I saw that you had already made comment about them so the only thing I can suggest is you look at faxing software for the Mac.
http://www.smileonmymac.com/PageSender/index.html
Pahu