What is confusing me is that a POT is one resistor.
A potentiometer is often manufactured as one resistor, but the wiper connects to some point along the resistor, effectively making it two resistances that are connected at the wiper. Some applications do not connect to one end, or connect one end to the wiper, so one resistance isn't used, but it is still there. Your application uses both ends.
Potentiometers do not have to be made as one resistors. Have a look at these:-
https://uk.farnell.com/bourns/3683s-1-502l/potentiometer-digital-5k/dp/1200095
Those are potentiometers, so the total resistance is what it is specified as. Each digit works by having two resistors, and one resistor is increased while the other is decreased.
If you have a 1 kOhm, 3 digit potentiometer, and it is set to 2 6 9, then the first digit has a resistor of 200 Ohms on one part and a resistance of 700 Ohms on the other.
The second digit has a resistance of 60 Ohms on one part and 30 Ohms on the other part.
The third digit has a resistance of 9 ohms on one part and 1 Ohm on the other part
The first parts are all in series, so that adds up to 269 Ohms. The other parts are also all in series so that adds up to 731 Ohms. The total resistance is 1000 Ohms.
Physically that is 6 variable resistors, two can vary from 0 - 900 Ohms in steps of 100 Ohms, but they will always add up to 900 Ohms. Two can vary from 0 - 90 Ohms in steps of 10 Ohms, and will always add up to 90 Ohms. The last two vary from 0 - 9 and 1 - 10 Ohms, change in steps of 1 Ohms and always add up to 10 Ohms.
You do not need to know about the construction to use the pushbutton potentiometers, because the total resistance is always 1000 Ohms, and the wiper can be anywhere from 0 Ohms to 999 Ohms from one end, just like a rotary potentiometer. If you were to want to replace the potentiometer when it was set to 269, you just need one resistor of value 269 Ohms and one of value 731 Ohms, and the pair would behave exactly as the potentiometer but would not be adjustable.