XOR in common programmer speech is ambiguously used to mean XOR or NAND, so I think their use of XOR was casually correct, while not technically correct.

While NAND is technically correct, it's just not commonly used as a grammatical conjunction.

It is?

I thought it was just used for, like, a couple jokes that you get from “intro to digital logic” class. The joke is funnier if it is correct, I think.

This may be among common programmers who don't deal with any bit twiddling or low-level stuff, but having worked on embedded and also on network stack stuff, it is certainly not the case there. Using the wrong term there will at best confuse your colleagues, at worst result in a logic error in the code, and a potentially nasty one at that depending on how common the low-low case is.