How do you decide this? In what way is Frye's game more "center-like" than Stoudemire's? Frye usually is assigned to guard the other team's most dangerous big man, but that's just to cut down on Stoudemire's foul trouble.
When Stoudemire and Frye are on the floor together, I see no rational reason to call one the center over the other. The truth is that neither is.
Like you said in your 1st paragraph Frye is guarding the other teams center, so he's at least doing something Center-ish. Amare isnt playing like a Center on offense or defense, so he's clearly not the 5. At least Frye looks like a Center out there 50% of the time.