If another user can do that on the same machine, it won't be an issue with the browser or the system itself (clearing the cache is always a good idea though). If a user is manager of that project, she should have all the necessary access rights. To indent a task under another, the task that is going to be a summary task must not have actual values (an error message will say that too). If that is the case remove the actual values (set task's state back to ready). Is time logged against these tasks? This all does not explain why another user with the same access rights is able to indent the task, of course.
This situation occurs even when adding two tasks and trying to indent the second one. The other resource is able to do the same thing without a problem (they logged into PPM with their own id on her machine and can update her workplan).