How does this work?
When moving fast enough towards the wall, if the kart lands precisely on the plane of the fence then you can pass through it (not over it).
How precise is this?
The fence plane is at -688.00. The kart's location can differ in as small as 0.000061 units. Pressing A for a single frame moves the kart 0.000488 units.
What are the chances of hitting this?
If you're just randomly aiming at the fence and firing a mushroom, roughly 1 in 90,000. You could attempt to position the kart more precisely to reduce that to maybe 1 in 15,000 but at the cost of a few seconds.
Why are you setting up differently than the TAS?
Many different setups are possible for the fence clip to work. Quite a few different angles and kart positions have been tested.
How much time does this save over the old shortcut?
About 5-10 seconds depending on how quick you setup.
Does this work with all characters?
Any character other than Bowser and Wario. You need to be moving at a rate larger than the size of the character when you get to the fence. Because Bowser and Wario are larger, there is not enough space on the train tracks for them to build up enough speed to be going fast enough to get through the fence.
I've clipped into the train tracks before. Did I perform a miracle?
Going from the outside of the tracks to the inside is significantly easier and not hard to replicate. It's going from the inside to the outside that is difficult.