False statements on a visa application is a federal offense and grounds for inadmissability. Presumably they clicked "no" to "have you ever been denied a visa" when in fact they had.
I wouldn't presume anything. There are lots of reasons this could have happened, and not just due to lying on the application. Perhaps they had not been denied the J-1, but were just having trouble meeting all of the requirements in time; a J-1 visa requires a whole lot of paperwork, including from sponsoring organizations, and if some of that was taking longer than expected and may not have been done in time, they may have just thought "oh, we can do the ESTA and stay for 90 days with no visa, during which we can work this out", when in fact that is not allowed.