Snooping is one concern, but the other one is the repair depot people may erase and reload the hard disk if they determine the problem is software (virus, trojan, etc.) So having a backup is critical.

In my experience, business product support is better at accepting a computer for repair without a hard disk. Consumer product support wants the complete computer.

I usually get a SSD to replace the platter hard disk that comes with the computer. The original hard disk keeps the factory OS which helps the troubleshooting process. I send the computer in with the original hard disk, and my data stays with me on the SSD.