I have a vague recollection that there might have been an agency by that name, but that could also be my imagination.  Somebody should grab it if it's not already taken.  

I remember.  Was a newspaper that you could get inside the Times Square sex shops that told you where all the nyc brothels were.  It was my go to back then.  Showing up in a random apt and then seeing a lineup.  Was great.  

If so, I actually do remember though never patronized.

Was it a movie or a night club ?

A high profile agency .  Never saw "Natalie" but some of the girls were amazing.  Especially a woman of Romanian background who was extraordinary!

I forget most of the titles, but there were several tabloid-sized newspaper / advertising magazines in the smut shops. The last time I bought one, it was probably $5. There was, of course, Screw magazine which had lots of classifieds.  
http://www.theeroticreview.com/discussion-boards/new-york-2/re-adding-to-inicky-265562
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The Village Voice was also more mainstream but had classifieds and personals that eventually became Backpage. I do not specifically remember NY Confidential.

I learned what NOT to do by learning about that long gone agency.  How to stay safe was doing the opposite

The "New York Confidential" escort agency was a high-profile, illegal prostitution ring that operated in Manhattan in the early-to-mid 2000s, founded by Jason Itzler after his release from jail on drug charges in 2003. In January 2005, police arrested him and others associated with the agency on charges of promoting prostitution, money laundering, and drug possession. One of his escorts known as "Victoria" in the agency was involved with then-New York Governor Eliot Spitzer, known as client #9, leading to the 2008 Spitzer prostitution scandal and later Spitzer would resign from his post as NYC governor March 2008. In March 2010, 21 year old college student Julia Sumnicht was found dead from a GHB date rape drug overdose at an apartment in Miami shared by a photographer and Jason Itzler who admitted taking GHB that night. Jason Itzler currently streams as MrBasedNYC on KICK. https://kick.com/mrbasednyc