Hide fusion core theme from users?

This can actually be done through Drupal itself and not the theme configuration settings. Check your Permissions page and either enable or disable access to those who can change the theme for their user. Admin will have the ability to change it but other users will only if you grant them access. Attached is a screenshot of those settings.

But what if you want them to be able to change themes but just not to fusion core? There should be an extra permission just for fusion core.

Why do you have Fusion Core enabled? It is perfectly safe to disable core to use a sub-theme.

Aside from this not being necessary, or maybe I am missing something o.0, creating an extra permission to do this would be quite hacky as there is not a good way to handle adding this permission.

I believe that maybe you thought you needed Fusion Core enabled to use a sub-theme so I am marking this fixed, if there is something else going on feel free to re-open and explain your situation.

[edit]
stephthegeek just pointed out to me that Fusion Core does need to be enabled to use the Skinr styles from Fusion Core in your sub-theme. To overcome this limitation you can just include the Skinr styles that you want within your sub-theme.

Thanks for the note, this is good enough for me.

You're welcome, glad I could help - also points to stephthegeek for pointing out the Skinr styles from parent theme