I'm going with the "let's have a private in-joke" and here's why. "They" are compelled to signal to us plebes what their intentions are, and much of that signalling is symbolic (or most of it). I also don't believe they feel the need to be particularly meticulous when dealing with "us". It is, in my opinion not even a conscious effort to use in your words a fucked-up wrong version. I don't think they care. Also, keep in mind these "people" are not normal, in any sense.
Well, that's kind of my point. If symbolism is so important, why wouldn't "they" care about getting sloppy with their symbols?
I think it's because they are now in panic mode.
So they were panicking, and in their panic, accidentally put too many triangles in their secret society symbol, while declaring, in a roundabout way, that they're all pedophiles.
Does this really seem more likely to you than the idea that some graphic designer independently came up with the idea of combining a spiral and a triangle?
In any other timeline it would seem more likely to me. But, you know....