After further tests, Inline editing isn't working for this user for any object. Although, the User Interface looks ok (actually - ALL CB's - but last three - are checked)
Inline editing is enabled:
UPDATE: It's not working in any view.
But on Custom Object - nothing
Suggested solution in SF site - My edit button is not overridden : http://help.salesforce.com/apex/HTViewSolution?id=000004555&language=en_US
I have tested with my user name: it works. than logged with the effected user on my machine: inline isn't working.
Edit option is available for that user, for that object.
I found another differance between the user's account and mine.
The top bar, on my account, is a drop down
While on the user's account, it's not
Although, the setting, which I think effects this, was reset in both, the user's account, and mine (to try and solve it)