I think I've heard that before. Picardo's concern may have been that his character would always be confined to the sick bay, and the challenge as an actor was to do the most with that. It also made the character unique, well even more unique, because of that limitation. The holo-emitter allowed him to move beyond those four walls, but in a way made him more like everyone else, thus "ruining" the character. If he can get around, go anywhere, then what's the challenge, what makes him different? The answer was, as you said, the Data-like arc wherein he, as an AI, learned to go beyond his basic programming.
In fact, Data was awesome but ultimately was a self-contained and finite AI. The Doctor, being a program, had the resources of the ship's computer to build with.