Please do not insult me by thinking I'm dumb enough to fall for the false water background and the stem background.
A 'false loop' as I like to call the problem. I'm sure you're aware of the loop problem with stages like Hyrule Temple where you can run away forever with no chance of being caught. You can do this with Hanenbow thanks to the terrible platform layout, with Fox actually being the problem again.
For the small amount of time that Fox will actually be running, his running speed is faster than most of the cast. However, the problem lies in his ability to have about 3 options for movement from nearly any position on the stage. His rising fairs and blaster jump (similar to Lucas' zap jump, only it makes his second jump significantly fast instead of getting an aerial boost) allow him to move from down to up faster than the majority of the cast. Then his falling speed allow him to go from down to up faster than the rest of the cast. His reflector is able to stall in the air to allow a quick change in the path he is running. His illusion will allow him to move between left and right incredibly fast, which he is able to do nearly blindly since the spots where he won't land on a platform are minimal. He will always be able to escape his pursuer after gaining the lead, which is easy to be gotten right away thanks to his blaster. And sadly projectiles won't be able to spot him and force him to fight, thanks to his ability to either reflect them or use the leaves as safeguards against them. He's able to easily wait at any point for where his opponent is going to approach from, and have a multitude of ways to react and run away.
It's very dumb. Simply go and test the things I told you against a person or even a CPU. See how incredibly easy it is to not be touched.
That's simply the extreme situation. Other characters are able to do the same thing, just not as well.