Before I explain exactly how he's wrong, here's a good rule of thumb: If an interpretation of a rule makes it completely useless, then that interpretation is probably wrong.
Now, into the nitty gritty details:
Firstly, the "Moving on from reserve" rules as described on page 136 make no mention of deployment zones, only the controlling player's Table Edge. This matters, because in a Vanguard Strike game, you can actually come onto the board from reserves outside of your deployment zone by moving in from the far right (or left, depending on how you deployed) of the board. (Also, fliers and some other models can move far enough to end their turn outside the deployment zone as well, even in a normal deployment.)
Secondly, the "Outflank" Special Rule on page 168 makes zero mention of deployment zones as well. This should really be all the proof you need, as specific rules override general rules. But, combined with the first point: There is no rule saying that, when you come in from reserves, you must come in inside your deployment zone. Furthermore, Outflank specifically says you can come in from the table edge to the left or right of the player's table edge, with no mention of other restrictions.
Frankly, it sounds like he just doesn't know how to play and was making things up, or else he was trying to get an advantage by tricking you.