You can move around while in hitlag. A directional input on the analogue or C-stick will move you slightly; this is called Smash Directional Influence (SDI). Additionally, on the last frame of hitlag, the current position of the C-stick or analogue stick will be converted into movement, but with only half the distance of true SDI; this is called Automatic Smash Directional Influence (ASDI).
Players have known about SDI and ASDI for a long time, but they have steadily seen more and more use, and for good reason: proficient use can make escaping combos much easier and even half-invalidate some options; Falco's up-throw is famously vulnerable to being SDI'd so hard that no followup is possible.
Fox himself suffers from this phenomenon, for his up-air can be SDI'd by skilled players to completely avoid the strong hit! Of course, there's always back-air...