Your information is correct in general, but there are many exceptions that prove the grandparent correct. My apartment was built in the last 10 years (i.e., after 1970), rents for close to $4k, and IS rent stabilized. See information here:

https://www1.nyc.gov/site/rentguidelinesboard/resources/rent...

Specifically:

"Also, some newly constructed buildings may be stabilized due to a 421-a or J-51 tax exemption even if the rent is $2,000 or more."

A program that a significant number of developers have taken advantage of.