I am not sure what the actual Putinists claim. My take is that Ukraine, Russia and Byelorus are in process od divergence (which maybe can be reversed to some degree) from the origial ethno/cultural unit called Rus. Rus, started in the north as Germanic tribe of Swedish Vikings organized Slavic and Finnish tribes into one society, first in the center in Novgorod then in Kiev. Then the east was conquered by Mongols/Tartars and west was conquered by Lithuanians/Poles. Later Moscow became the center of revival.
Galichan theory was fabricated in XIXc Lvov and denied Russian claim to be the continuation of Rus, at the same time Galichans framed the history of Ukraine as victim of Russian invasion. In such view the actual history of Rus from IXc to XVIIc is losing any sense. It is very sad to base one's national identity on a lie.