A compressed image which does not reconstitute to the original image is by definition lossy. You can't scale a PNG down by 25% and call that "lossless compression".

Though I'll gladly take your logic and call the first 1/64th of a progressive JPEG lossess (which it is, since at that point you only have the DC offsets of basic blocks, which undergo no lossy compression).

I think JPEG's color transform is lossy, so even those basic blocks are somewhat lossy. A better approximation of the entire 8x8 block than the exact pixel at the top-left position of the block, which is what FLIF and PNG with Adam7 interlacing do, but still lossy. If you would take an image, magnify it by a factor of 8 in both directions so each pixel gets blown up to an 8x8 block, then convert it to JPEG, there is still some information lost.

It's lossless (in theory) when compared to a 1/64th scaled version of the original image (which is what was clearly meant).