You are correct, manual sharing is available for the record owner, any role in the hierarchy above the record owner, and the system admin.
From Salesforce ,
You might not see the button if you’re not logged in as the candidate record owner or system administrator. The button is available when your organization-wide default for candidates is set to Private or Public Read Only.
So you might have confirmed that the
sharing button is available when you logged in as admin. Try going to
Manage Users|Users and login as the requesting user, or ask him to confirm that he can see the sharing button.
If the sharing button is not available, make sure that
Manual User Record Sharing in
Sharing Settings is checked.