Don't blame Tennant for that, Richard T Davies was just a damn terrible writer.
Indeed and its something to remember allot of the time when an actor is blamed for something silly, if they're acting a certain way often its because the director/producer has told them to do it like that, or decided something has to be a certain way.
The same thing can be said for actors being praised for their acting, often they would have nothing without the actual writers to pen the lines for them to deliver or to write the scenes for them to act in.