Watch out because I was burned by this same type of situation. I bought a 300mm Nikon lens grey market. Two years later, an internal element CAME LOOSE, the only time this has ever happened with any lens. The lens was perfect when I left my studio, but apparently while I was wheeling my lens case across the parking lot to a baseball game the element came loose. Maybe vibrations from similar situations over time caused this to happen.
Anyway, the only available repair locations Nikon permits are its two national service centers. I was told by phone that even if not under warranty, I could still pay full price and have it repaired. So I insured the lens and shipped it to Nikon... bad decision.
After an 8-week debacle and hours of wasted time on the phone and email, I finally got the lens back from Nikon, completely unrepaired. They absolutely refused to do anything no matter what I paid, because it was imported from Japan by a 3rd party.
I have heard that sometimes Canon U.S.A. will repair gray market lenses as a courtesy only to some customers who pay full price. And I know for a fact that Canon's customer service is close to a 10 out of 10, while Nikon's is close to a 0 out of 10. So my horror story probably wouldn't have happened if I was working with Canon.
But in general, gray market lenses will NOT BE REPAIRED unless you ship back to Japan, and local repair centers may not be trustworthy.
The problem in my case was that I could not even ship back to Japan, because Japan required the ORIGINAL paperwork that B&H Photo Video had when they imported the lens from Japan, and of course B&H refused to provide me their wholesale bill of sale from Japan.