I'm not sure I actually agree with that. There is just so much to learn from experiencing other games. It would be like saying you can be a good cook if you ONLY cook food from one country. Yes, you might cook that country's food really well, but, it's an extremely limited palate. No chef worth the salt would ever claim that only learning to cook Mexican food (as an example) is a good way to learn to cook.
Heck, even the idea of driving. Sure, you can learn to drive only driving one car. You might really like that car. You might even drive pretty well with that car, but, unless you actually experience driving other kinds of cars, you aren't a good driver. You can't be. You can't understand why other drivers do what they do without having any experience with those vehicles.
Variety is, as they say, the spice of life. I've learned FAR more about how to run a game from running other systems and then coming back to D&D than I ever learned from just running D&D. Whether it be stuff I want to do or stuff I don't want to do. Either way.
So, no, I don't think you can be a good player or a good DM without ever trying another game.