Ha, that's oddly very similar circumstances to a scenario I had in my IT support job several years back in TN. At that time the state agency I was employed through had moved to these large Lexmark MFP printers on roller carts, and one of the small county offices was having a semi-consistent issue with faxes not coming through. Our contracted Lexmark service support came onsite, could find no issue with the hardware. Local telco was contacted, they came onsite and both brought their own device to test with as well as hooked up the old standalone fax back in the storage room, and everything tested fine there. Both angles were pointing fingers at each other. Finally someone in state office got in contact with higher level management on both sides and arranged for them to come onsite together along with me so we could all try and figure out what was going on.
Turns out the newer technology in the MFP required a higher voltage threshold somehow coming off the 'ring generator' downline in the phone system, they finally traced the issue to said ring generator in the equipment that serviced the block area this office was in. The ring generator hadn't gone bad, but it had deteriorated just enough so as not to provide the proper power through the line to trigger the MFP to pick up on/recognize it had an incoming fax attempt. Soon as they replaced the appropriate piece of hardware, all was resolved.