Yes, the puzzle is 100% solvable with low-res picture, as initially released. The fact that while zooming in you can find certain things is the cloud-effect playing on you. There are hidden things left on purpose, like the rabbit, but these are all clearly visible with the original JPEG image. TIFF/hi-res-JPEG were released only so people stopped following JPEG-related compression artifacts NOT so you can zoom-in 1000% to find hidden birds singing songs to you.
Exactly as you said.