Not quite. You can tell this isn't true because there are many common images (game graphics, text, pixel art) where upscaling them with a sinc filter obviously

Not quite. You can tell this isn't true because there are many common images (game graphics, text, pixel art) where upscaling them with a sinc filter obviously produces a visually "wrong" image (blurry or ringing etc), whereas you can reconstruct them at a higher resolution "as intended" with something nonlinear (nearest neighbor interpolation, OCR, emulator filters like scale2x). That means the image contains information that doesn't work like a bandlimited signal does. You could say MIDI is sort of like that for audio but it's used a lot less often.