One of my coworkers has this problem for some of the files stored in a document library. If he clicks on the link, from the document library, the dialog has these two options: "Read-only" and "Edit" - once excel opens the file there is no "Check out" button at the top, nor is there an option to check it back in on the backstage view. For other files he gets the normal options: "Read-only" and "Check out and edit". This only happens when clicking on the link; if he clicks the arrow for the drop-down menu and selects "Check out" from Sharepoint before clicking the link he can then edit any document and can check it back in after.
Why does that happen for some of the files? I looked for similar problems (looks like they're quite common, despite the lack of solutions) and the only answer was to check whether he's using Internet Explorer 64-bit.
He is using Office 2010, Sharepoint 2010 and Internet Explorer 32 bit. All the files are .xlsx files.