You are correct. When someone applies for a liquor license in NJ they must provide a list of all individuals (or corporations) that own a significant percentage of the applying entity. Background checks are performed on those individuals and certain conditions can cause their license to be denied or suspended. Licenses come up for renewal annually and, generally speaking, the background checks are not done for renewals, but the license holder is supposed to voluntarily disclose any conviction that would have caused their license to be denied in the first place.
Adding: NJ liquor license laws are incredibly outdated and there has been discussion about scrapping the existing license process and starting over. A municipality can issue 1 license for every 3,000 residents.. People think of New Jersey as being urban, but in fact, other than some metropolises such as Newark, Jersey City, Camden and a few others, the state is made up of hundreds of small towns - many with fewer than 10,000 residents. So maybe 2 or 3 liquor licenses (and that includes liquor stores and bars/restaurants) are permitted in a town.
The result is that a liquor license sells for hundreds of thousands of dollars. Many establishments can't afford that (or a license may not be for sale at any price) so there are thousands of BYOBs. BYOB is nice if you are looking to save on the cost of a night out, but because wine and liquor have huge profit margins, that means the business has to survive on the sale of food alone. And while the BYOB only extends to wine (and perhaps beer) people do bring in their own spirits even if they aren't really permitted. If that happens, a restaurant owner/manager has to decide if they are going to look the other way.