I believe they believe they have a solution however based on what is publicly available I don't believe they are correct.    Still I don't see much sense in communicating privately.  I rarely sign NDAs and I can't remember ever signing one when I wasn't being compensated.   Even with compensation I doubt I would be willing to sign one as I would find it very frustrating if the code confirms my suspicious and then I am unable to use that code to support an argument.

Eventually the code will be open sources and we can debate it in the open.   At this point I can't definitively say the NXT team and their unreleased code hasn't solve the nothing at stake problem.  My argument is more than it is dubious to claim something is solved based on secret code.  The public can't independently verify that claim, nor can they look to skeptics for a counterargument.  I believe in Bitcoin but I do read articles written by skeptics but they are an outside viewpoint and sometimes that is useful.