I believe you are confusing this with the recovery key of the 2FA of an AppleAccount. But this is not what is meant here.
We are talking about the recovery key that can be set up during the FileVault encryption of the Boot Volume.
Usually the boot drive is decrypted (=unlocked) with the login password, but the volume can also be unlocked with the recovery key.
If OPs daughter went through the usual Login Recovery steps, she will be asked in Recovery Mode for this FileVault recovery key.
The link you posted is not correct for this topic. We are talking about the login for the Mac, not the login to her Apple Account.
@OP:
Ask your daughter to reboot (or startup) the Mac and try to login again. Ask her to look into the right upper corner of the login screen and have her check if the correct keyboard layout is selected.
I had so many problems with "non-working passwords" just because the keyboard layout had been switched from German (my home country) to US somehow.
If that doesnt help, have her follow these steps:
If you can’t log in to your Mac user account, try these solutions.
support.apple.com