"If it were a fact, it wouldn't be called intelligence."

I think the other way to read it is that you're fundamentally going to have to choose (by your freedom to control your algorithm's design) which of the maps from (2^|x|) -> (2^|compress(x)|) are the ones that actually end up getting no compression (ie |compress(x)| actually > |x| - bc of pigeonhole principle) and which ones are the ones that do get to be called compressed. So you do have an implied kind of lossiness w.r.t. to what parts of the input domain are actually compressed.