I usually don't use the View Cube but thought I'd test this issue to see if I could replicate it. Sure enough, with the Extrude dialog open and the Depth field active, when I rotate the VC the Depth value will change. As soon as I Tab out of the Depth field and it is inactive the values stop changing as I rotate the VC.
I also saw that if I click and drag anywhere on the workspace that will change the Depth setting. You do not have to select the drag arrow on the model to change the depth. It looks like the entire workspace becomes active and allows a click and drag anywhere to change the depth.
It has been noted before on the forum that there is something about the VC overlaying the workspace that the workspace is still "active" behind it. So what you are seeing is a known issue with the VC and, I think, has been sent to Dev. Maybe @DavidJ
could comment on that.