I think it is section
16.1 & 16.2 here which are applicable.
16.1. Changes to bookings for Reward travel on flights operated by British Airways or Airline Partners are permitted only in respect of date, time, class of service and (subject to Clause 16.2.) route. Such changes may only be made by the Member or an individual nominated in accordance with Clause 3.13. If more than one Avios and Money price option is available for a British Airways flight, it is not possible to change the price option chosen by a Member after a booking has been made. All permitted changes are subject to capacity limitations and may not be made after the time 24 hours prior to the scheduled departure of the first flight in the Reward travel itinerary. A fee as specified on ba.com may be payable for each permitted change. For the avoidance of doubt, name changes are not permitted.
16.2. The route applicable to an Reward travel booking may be changed provided that the new route selected would, as at the date the change is requested, require the redemption of the same amount of Avios Points as was redeemed in making the original booking. Route changes are only permitted for Reward travel bookings which (other than for the payment of taxes, fees and charges) are purchased using Avios Points only.
The change of route part is correct for what you have been told - I know that PHX and DFW are slightly further than ATL but they will all be in the same band and that is how the avios levels are set. Actually, I don't think you would be able to change it anyway as 16.1 clearly states:
All permitted changes are subject to capacity limitations and may not be made after the time 24 hours prior to the scheduled departure of the first flight in the Reward travel itinerary
This was what I thought as well, so at less than 24 hours or once you have started flying the booking you can't change it anyway. Cancellation is the same, less than 24 hours and you don't get any avios refund.