> so doesn't some interchange between me and the person i'm calling ultimately decide what frequency carrier the receiver hears?
Probably it's an interchange between your POTS handset and your local phone service provider's head-end, that determines the "media type" of the call; and then, in the case of fax, that call is forwarded (including media type) to the other land-line's service provider's head-end, where the service provider then negotiates+accepts the media type, rings the fax on the line until off-hook, and then sets the opened line to operate at that frequency.
I'm guessing that the thing picking up the carrier on the sender's head-end is the same thing that parses DTMF tones off the line; and therefore, not a component that exists in the signal chain of cellular service providers.
(A similar thing happens in cellular voice signalling—the negotiation of a voice codec—but it happens out-of-band, not in-band, AFAIK—on both ends (like a web browser talking to a web server) unless one end is POTS, in which case the cellular voice provider jumps to the POTS network with a DAC+bank of line couplers. In theory, this means that a cell phone might be able to send a fax to a fax machine, if there was a special voice codec option in GSM/CDMA/VoLTE/etc. for "lossless 56KHz PCM", that would be decoded at the POTS gateway into a raw line signal.)