You're right, it probably isn't a coincidence. Playing without Steve Nash in each other's primes probably has something to do with it in Amare's case. Amare, a scorer, leaves the Suns who always had a great PG feeding him throughout his time in PHX, joins Melo, another scorer who demands many shots.
PHX: Great PG, Amare consistently main scoring threat on the team
NYK: Less than solid PG, Amare + Carmelo Anthony, +injured during this Lin stretch
It's really not a coincidence. I think D'Antoni is probably doing some similar things, but the situation is much different compared to Amare's days in Phoenix.