That is false. In NY state, it is legal to purchase, possess, and wear body armor. It is illegal to wear it while committing a crime. Which is stupid, since you already happen to be committing a crime, I'm going to go ahead and say you don't really care about the extra felony there.
From the NYS penal code:
Section 270.20 Unlawful wearing of a body vest
1. A person is guilty of the unlawful wearing of a body vest
when acting either alone or with one or more other persons he commits any
violent felony offense defined in section 70.02 while possessing a firearm,
rifle or shotgun and in the course of and in furtherance of such crime he wears
a body vest.
2. For the purposes of this section a
"body vest" means a bullet-resistant soft body armor providing, as a minimum
standard, the level of protection known as threat level I which shall mean at
least seven layers of bullet-resistant material providing protection from three
shots of one hundred fifty-eight grain lead ammunition fired from a .38 calibre
handgun at a velocity of eight hundred fifty feet per second.
The unlawful wearing of a body vest is a class E felony.