> Maybe each khipu user had their own system for encoding non-arithmetic data as khipu numbers, so that each person's khipu was incomprehensible to anyone else.

That is the sort of things linguaphiles do, like JRR Tolkien, and certain highly neurodivergent people, but in general that's not something a general population would do.

By definition, it still wouldn't make them literate even if true: "I can only read and write my own writing."

It's actually very common in our own society for children to make up "secret codes" for their own use or to communicate with a single friend, and notation systems limited to a small affinity group are fairly common even in societies like ours where they have to compete with a standard written language: baseball game records, knitting notation, cross-stitch notation, chess notations, mechanical dimensioning and tolerancing, electronic schematics, shorthands, cement chemist notation, Perl, hobo signs, and so on. If you've ever worked in a company that is more than a few years old, even something as small as a diner, you can probably think of two or three notational systems used only within that company. In our society, at least, it's not just highly neurodivergent people.

I don't agree that being literate in a writing system nobody else uses is equivalent to not being literate.