Yep, the tweeter level and even the shape of it's output is controlled by the crossover, and ultimately the speaker designer. I could easily adjust that on any of the 3 different models I listen to at home.
The overall balance also matters a great deal. It's not just what the tweeter is doing but what the bass is doing, as well as the crossover point and therefore radiation pattern, so it is important to hear speakers for yourself, in an environment similar to your own.
This may have been JA's failing in the case of the Diamond's. He set them up with poor bass, and he attributed it to excess mid/treble energy.
Best,
E