I am fairly sure it would be a crime for the President to pull up someone's VA health records on a whim, or at least it would be a crime for anyone at the VA to facilitate him doing that.

We can also add to that IRS data. The articles of impeachment against Nixon included the following:

"He has, acting personally and through his subordinates and agents, endeavoured to obtain from the Internal Revenue Service, in violation of the constitutional rights of citizens, confidential information contained in income tax returns for purposes not authorized by law" (emphasis mine).

There actually are laws regulating the handling of personal data collected by the government and it generally doesn't have a "the president wants to see it" exception.

> What data in a federal agency could the chief executive not have authorization to access?

Personally? For starters, he can't access anything the Legislature's laws say he can't.

The Executive is there to implement the law, and that includes obeying them him/her-self.

A President telling other people to break the law on his behalf by threatening to fire them is also a crime of extortion.

I think the question is whether employees of an advisory group that is not an actual department of the government are on the list of people to whom can he authorize access to this type of sensitive data.