The way I understand it is that visas are issued by the State Department, who go by answers to the questions. The actual border control is run by Homeland Security, who are the people who want to know your full history. Either way, the ESTA is issued by the State Department, and their questions are there to weed out people who need a visa. If you can answer the questions truthfully and still get an ESTA then that is good enough. On the Unlock website here
, they advise working from the questions. The Unlock page here
says that the government has confirmed that they don't share that sort of information with the US or anyone else. The recent news about sharing information was about US citizens convicted in the UK and UK citizens convicted in the US. You might well get a visa in time to go to New York, but why take up all that time and money to get something the US authorities have already said you don't need?