No, it doesn't necessarily get it from the tee command, and it always gets it from the shell when the it is called. I can think of three circumstances where it does not.

• If the shell can't execute tee, the error code would not be that of tee.
• If the shell exits due to a signal or a core dump, the error code would not be that of tee. (Right?)
• If the script runs under Windows and tee returns an error code greater than 1, the error code returned would be 1.