As long as the tube was not epoxied into the case, you should be able to unscrew it with a Rolex case tube tool or rat tail file (small, 3-sided hobby file). Unfortunately, if the hole was countersunk/drilled too deep, short of welding new metal in there, I do not know of any way to reinstall the tube 'higher'. Though, if you are careful (& lucky), you might be able to fix the tube into the case at a more appropriate level by epoxying the tube into the case. I would use a slow-drying epoxy so you can make corrections before it dries.
Adding to By-Tor's comments -
When new, the crown on most Rolex watches screws down close to the case. However, when they (Rolex) replace the tube during a normal service, the new tube is often installed so that the crown sits slightly proud of the case, which leaves a noticeable space. This is why I install the tube in all of my Rolex watches similarly (with a space). I think it adds a bit more credibility to a watch since reps tend to have their crowns screwed down against the case.