Okay, so one of the new flagship features of Illustrator CS6 is gradients on strokes, but you can't use the Gradient Tool with them? I just get a crosshairs pointer with a "no" sign next to it. What's up with that?? I can see why this wouldn't work with shapeburst mode, but linear and even angular gradients (to set the center point) should be no problem.
In addition to this, here is another bug I discovered:
In earlier versions of Illustrator, you were allowed to use the Gradient Tool to adjust the direction of a shape's gradient even when the shape's stroke was in the foreground. Now that Illustrator can apply gradients to strokes, it is understandable that, if a shape has a transparent stroke, Illustrator will prevent you from using the Gradient Tool on the shape if the stroke is in the foreground.
But the opposite should also be true: if you have a shape with a gradient stroke and a transparent fill, Illustrator should prevent you from using the Gradient Tool if the fill is in the foreground. But it doesn't. Illustrator will happily respond to the new gradient direction, but the gradient of the stroke will not change, and the fill stays transparent.