This seems to be true in my experience. I was stopped in a subway station with a legal folding pocket knife (no assisted opening, blade length <4"). One of the undercover cops took the knife and repeatedly tried to get it to open due to gravity alone but couldn't. While he was doing this, the other one was questioning me: what do you use the knife for? (opening boxes at work) what do you do for work? ("computer guy").
They gave it back to me and told me it's best if I keep it inside my pocket instead of clipped to it.
Even though that ended OK for me, there are a bunch of ways it could have gone worse. If either cop was an asshole, or having a bad day, or if I had darker skin, or was wearing a hoodie, etc. I once read about someone getting locked up overnight despite his knife being legal because he had it clipped to his pocket - the visible clip was deemed by the police in that instance to constitute "brandishing a weapon". Not sure if that's true, but probably best not to take chances.
The word "gravity knife" has slowly become any knife you are carrying seen by the NYPD. I am being slightly flippant but not really.
The law is completely ridiculous, there are tons of cases of brown people receiving prison terms because they were carrying a knife for work.
There are actually a lot of stabbings in NYC daily, so politicians are not motivated to repeal or clean up the language in the gravity knife law.
In 2016 the ny state assembly and the ny state senate passed a bill to repeal the NYC gravity knife law, but Governor Cuomo vetoed it.
http://www.villagevoice.com/news/how-a-50s-era-new-york-knif...
https://www.nytimes.com/2016/05/31/opinion/new-yorks-outdate...