That rule #1 doesn't quite apply in this situation.

That you should never need to give out passwords is mostly a safeguard for social engineering and phishing scams for accounts stored on a server over the internet. Only a malicious third party would ever ask for these types of account passwords, because those with legitimate needs to access it (you and the service operator) already have it (hopefully just the hash in the case of the latter).

The password you're referring to here is an encryption key for a local hard drive that nobody else has access to. If they do in fact need access to the encrypted OS partitions stored on your hard drive in order to diagnose your problem, then they have no choice but to ask you for your encryption key. That's cryptography working as intended.