The user doesn't have access to one or more CSS files, most likely corev15.css is one of them. To confirm, you could use Fiddler or the F12 developer tools in the browser to record the network traffic to see which specific files to showing an access denied message.
But let me take a guess: Corev15.css is available to all users by default. Perhaps someone tried to modify it and made a copy of that file and the user doesn't have permission to the copy? Perhaps it's as simple as the fact that a copy of corev15.css has been referenced, but the corev15.css file is not checked in, or doesn't have a major version published/approved? Again, this is a guess, the better answer is to use fiddler or f12 tools to track it down. So:
- hit f12, which should open the developer tools in a panel or a separate window.
- Switch to the "network" tab.
- click the green start button.
- refresh the browser window
- watch in the developer window/panel as every single network call is displayed. Look for calls to CSS files that don't have a result of 200.
If you identify a CSS file that is not loading successfully, you'll need to find out why. Again, common issues are the file not being checked in, not having a major version published or approved, or permission issues.
edit: here's the menu to get to all site content: