Lossless compression of non-random data is very possible, though. Video and audio files are far from random, and I don't believe that lossless compression is "a solved problem" (even by the business standard) for those. (However, it is a bit far-fetched that someone would invent a groundbreaking new algorithm in the space for a silly website.) General lossless compression may not exist, but we're talking about highly patterned (low entropy) subspace of all possible files/bit-strings.

Lossless compression requires assumptions about the data, of course, because making some patterns shorter requires making others come out longer. Random data will, in general, get larger under a lossless compression algorithm.