A few rather simple questions:
Which Polish government?
What region and time?  
What regiments (Polish and Soviet). If regiments/or/if partisants? And finally how about Warsaw uprising (just an example to show, how generalization can go utterly wrong, was not ment as an insult).
Continuing about units - or rather - direct question were AK units fighting Soviet partisans or not? 
Further Questions - what weapons, uniforms and helmet do we see in the Image:Comp_obwSambor_inspecDrohobycz_Burza3.jpg

Regarding the second issue:  
Just two citations on  Piotrowski:
 By mediator on this article: Denying author as a third party source: see this 

 From the peer review of his book: As stated above, the book nearly ignores the Soviet and Nazi participation in the Polish holocaust.  After a very brief description of the economic, social, and human atrocities committed by the Soviets and Germans, (constituting only 25 pages out of a total of over 250) Piotrowski delves into the manner in which Poland’s largest minority populations attempted to exploit the upheaval of war.  

I'll not go into further conclusions, the review says it all: sometimes the book does seem, as if  AK did not fight against Germans, but more against minorities in borders of Second Polish Republic.