These kind of claims are always hard to respond to. We have the hotel guest, who we have no idea how she checked in. Did she reconfirm with the hotel that the check out is 4PM or did she just trust you had taken care of things? I'd assume the later. You seem to be the guy who wants to care of other things and she trusted you and just asked for her key and that's it.
I'd never let anyone make my reservation because each one of us have our own preferences and would advice you not to do so in the future.

So the FD had no information from her upon check in that she asked for a later check out. This is crucial. If you don't ask or reconfirm (if you asked earlier) for a later check out upon check in you are not given a later check in.
Has never happened to me at least if I don't reconfirm with the hotel upon check in that I'm granted later check in. Even if I request and the hotel confirms by email that it's possible many days earlier.

Don't book for other people when you are not in their party or stuff like this happens. If she had done the booking herself she would have taken a more adult responsibility and had reconfirmed with the FD her requests.