They can't boot it off a flash drive? I can understand asking for a password to do that, but the system should not be designed so that they need access to the current OS install to diagnose hardware problems.
Who said it's a hardware problem? When my logic board was replaced recently, I had horrendous issues for a few days, with Chrome unusable, high CPU usage, etc - something was funny with the drivers, and it took some command line mucking about to fix the issue.
Had I given them my password, I'd not have had the issue. I was able to do the fix, but not everyone would be able to.