When you play quickly on a heavier piano, your fingers are likely bumping keys that you aren't actually playing, and it is fine because the weight of the keys is enough to keep the note from sounding. But when you make that same motion on light keys, the slight bumping of the key will be enough to sound notes that don't belong in the music.
True. Following this line of thought I would like to add another. Personally, in my experience when playing from my heavy piano and transferring to a very light one (another grand piano at the college with very light keys) there is also the issue of uneveness of the volume of each note.
This uneveness become very noticeable when doing piannissimo (either fast or very slow). A very heavy piano (with a low volume or whatever the technical term for that) will hide the little uneveness in your strikes to the keys while a very light piano will magnify them.
Example, a simple prelude in C by Bach from the well tempered clavier. I practiced it on my heavy piano, ok, I'm good. Then I play it on a very light piano where the slightest touch reverberates throughout the room. Suddenly I'm bombarded with an uneven ugly piece (especially the soft parts) therefore I had to quickly adjust.
BTW all my examples aren't just illustrations, they actually happened to me.TBH, right now when I'm checking for evenness, regularity, proper volume allthroughout I play on the lightest piano (like my digital) then I go to my heavy piano. Heck, I just switch between them regularly.