Those claims that the Polish Berling, or the 1st Polish peoples army as it was called in the soviet union were manned largely by Russians is not true, but the claim that the commanders were mainly Russian is true. also you have to think that there was two "polish" governments in exile. one was made from parts of the original government, and the other was a communist puppet government made up by the Russians, and they were always trying to make the other look fake.
most of the troops in the 1st Polish peoples army were prisoners of war who were captured by the soviets during the September campaign. This is a quote from a article about the amount of POW's the soviets had... "they had identified there were three main Polish prisoner camps at Starobielsk, Kozielsk and Ostashkov that housed 11,000 POWs. Starobielsk and Kozielsk housed officers and all the camps were abolished in 1940."
now the commanding officers of The 1st polish peoples army were in fact Russian, and the reason for that is after the September campaign the Russians began killing people they deemed a threat, and they ended up killing all of the military officers who had surrendered this another part of the article that talks about the Pow officers... "Concerns mounted when it was evident that no one knew the whereabouts of the inmates other than some 300 officers had been detained at the Pavlischev-Bor camp before being moved to Griasoviets."
This is a link to a website about the 1st polish peoples army http://www.polandinexile.com/ppa.html
I hope I have answered your question.