I highly doubt archive.org intended that association, it merely explains why a person would view it as an odd choice if words.
I find the fact that it is a fake chat pop-up a lot more untrustworthy.
Edit: Not sure why the downvotes for what is basically a candid, “hey if you’re confused about the wording it’s because it’s a very specific political activism shibboleth.”
https://en.wikipedia.org/wiki/Tongzhi_(term)#Usage_in_contem...
But if you lean into it and say something like “yeah obviously, I want that big Mao Zedong” observers know that you’re being absurd but the accusation just rolls off and now you control the direction of the argument.
This is basically how to publicly engage with people who argue in bad faith 101.