The actual power being used here, the Congressional subpoena power, doesn't have anything to do with whether something is public property or not, so that isn't

The actual power being used here, the Congressional subpoena power, doesn't have anything to do with whether something is public property or not, so that isn't the basis they're claiming. It's a general quasi-judicial investigatory power, which can be used to compel any person to both appear physically, and turn over any documents in their possession that Congress, in their sole discretion, believes might be important to decisions made by Congress. That obviously has significant scope for abuse, which is why Congressional subpoenas tend to be controversial, especially if they're fishing expeditions.