No, you are wrong. All of those flights, and all flights on the Moscow-Havana route, follow the great circle route because it is the shortest distance. Flights that must divert for winds or turbulence or scheduling follow a modified great circle route.
Today's Aeroflot 150 does not follow a great circle route, modified or otherwise. Such a deviation has nothing to do with weather or other environmental factors and can only be explained by a need to avoid a particular airspace and the potential for diversion to an alternate airport within that airspace in case of an emergency.
You will notice that the route overflies the Azores, Bermuda and Nassau so that those airports, rather than airports in continental North America, can be used as alternates when filing the flight plan.
This is the most telling aspect of the diversion, even more so than the diversion from the great circle.
Someone important who needs to avoid the airspace over North America at all costs is on that plane.