First, it's faster, easier and less intrusive.

The tenant only has one bathroom, and I'm trying to figure out if I should just match his paint (flat, which is the whole problem) and repaint the corner to be less intrusive or if I should go ahead and paint the whole thing semi-gloss to take care of the problem.My main concern is taking a day to paint his entire bathroom where he'll pretty much need to be gone.

Usually settle with various parties, insurance companies are involved, high 6 figure to 7 figure kinda stuff, often water intrusion.  

“The inspections are also significantly intrusive.

I am aggressive about water intrusion on my rentals and most policies limit the coverage for a large event.  

I feel bad and intrusive asking people for so much information.

@Jimmy Chao regrading to get water away is always a good idea but I would recommend having a water intrusion specialist confirm that the source is in fact the gutters as it could be a combination of gutters and/or stucco/grading/windows/roofing etc. best of luck!

Is this the wrong approach when it comes to being intrusive?

If your tenants are like me, they care more about minimizing the time intrusion than how many people are walking through.  

You'll probably have to take the drywall/plaster down to the studs too because of mold from water intrusion.