> I don't understand where I'm wrong about the 2x bw though? ... single leg squats will get you to 1x + 1x bw, which is 2x

The disagreement is purely about notation.

In the strength world, people routinely ignore bodyweight when measuring squat intensity - they only list load weight. I suspect that this is, in large part, an effort to be consistent with other barbell exercises like Deadlift (which I mentioned earlier), Press, Bench Press, Row, etc. where including one's body weight wouldn't really make sense.