Right, I see what you're saying now.
I'm going to think aloud here...
The grounds are common, we can take that out of the equation, because we're only interested in the amount of resistance between lug 3 and wiper (lug 2)
If the pot is being fed from the board via lug 3 (ie "IN"), then that's what I would switch out, as opposed to the wiper.
Looking at some of the diagrams I've posted, with the wiper common going to the shared output on the board, signal from the active pot looking to swim upstream after hitting the board and finding another path (to the inactive pot) goes upstream but cannot complete the circuit because inactive pot's lug 3 isn't connected...
The same works if the wiper is what's switched. Either way, signal cannot close the circuit.
So I join you in asking "why, indeed, would the pots need to be doubled?"
[EDIT:]
When people double the value of the pots, they're still making a circuit that works, albeit it behaves differently because of the different mod-value of the pots to stock.
Two equal-value resistors in parallel, the value is halved; but the pots aren't of equal value (presumably you don't want to change to the same setting in pot-b as in pot-a). That would take me into online parallel-resistor calculator land to figure out what they're doing, but since the circuit isn't closed on the innactive pot, the point moot if not mute.
Something to play with on the breadboard and see if there's audible differences between two different sized pots, stock and doubled. What the hell, throw it on the oscilloscope, too.
Ahhh but, in my making lug-3 the switched part of the circuit, when the signal swimming upstream on lug 2 gets to the "inactive" pot, some of it IS going to go to GND and complete that side of the circuit even if it can't do anything at lug 3.
So we cannot ignore ground as I first assumed. At least not the way I wanted to swap out lugs (L3).
So back to the wiper...
I shouldn't try this when I haven't slept all night.