Bizarre situation. I've never had an issue with security at JFK not accepting an OLCI home printed boarding pass, on any airline.

My hunch, and it's just a hunch, is that this is Aeroflot's doing, since, while I suppose you could mock up your own fake boarding pass and use it to get through security, you could do that with an Air France, or Delta, or whomever BP as well, so if that were TSA's actual concern, they wouldn't limit it to just Aeroflot.

Occam's Razor says that Aeroflot at JFK, for some reason (likely that they're not set up to passport check at the gate) wants you to go to the checkin counter.