Others claim that with the proper technique playing on a heavy piano will not be dangerous
That said, in general, if you practice on a heavy piano, you will be able to play on anything.
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.
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.