"In fact my landlord cited the increased median rent in the neighborhood as a reason to raise my rent."
Your landlord lied to you to get you to pay the increase. You had little choice because finding a cheaper apartment probably wasn't possible/desirable and you probably didn't want to argue with him in front of the rent board. Understandable but that doesn't mean your landlord's explanation has any validity.
You're saying that even though landlords may justify rent increases because of new constructions, if new constructions hadn't been built they would have used a different justification? And the rent increase would have increased just as much?
That's possible!
Maybe the rent increase is independent of that single new construction. Or it could be mixed depending on the type of housing. I looked into it a bit more[1] and it seems like lower-quality apartments near a new build go up in price but high-quality ones go down in price.
[1]: https://nlihc.org/resource/new-construction-has-mixed-short-...