As many others have so aptly noted, the Administrator in your anecdote was correct. The point about subject vs. object has been so concisely explained that I won’t repeat it.

Try to think about it this way. “Her” is always possessive: her degree, her resume, her partner, her job, her kids. It explains or modifies the noun that follows. If you think about it that way, you can understand how illogical it is to say “her went with me on vacation.” Or “her & I” drove to the hospital. (Yet, it would be perfectly fine, however, to say “her sister & I went on vacation” since her is paired with a noun. In that instance, her is used as the possessive that makes sense of, or modifies the noun “sister.”

I hope that helps.