Mangia un pomodoro can mean (1) he eats a tomato or (2) she eats a tomato, right?
That is correct
If you were waning to specifically say that "she" ate something, wouldn't "Mangia un pomodoro" be incorrect?
I think so.
without the pronoun, "mangia un pomodoro" is very vague. This could be he or she, but could also be the command "eat a tomato" I think it is misleading to have it here like this as correct.
I agree with the comments. You should accept the one with the pronoun LEI