This is patently so. Taken to absurd proportions, you can compress a specific rendition of the Mona Lisa with just one bit. 1 means Mona, and 0 is undefined behaviour.
Taking this a step further: 0 means that all subsequent bits contain an arbitrary PNG. Now your algorithm encodes any image, and still does Mona Lisa in one bit.
It's also almost as effective as PNG (plus one bit) for non-Mona Lisa images.