Actually the statement is false. In fact the VVS supporting the Red Army didn't have to fight against the Polish Air Force almost at all.
Firstly, there was the order of the Supreme Commander of the Polish Army saying to not fight with soviets unless they would attack our troops or try to disarm them.
Secondly, the PAF didn't have too many squadrons at the eastern front and these that were there, were mostly remnants of the Pursuit Brigade destroyed in battles with the Luftwaffe. There were the only 46 PZL P.11 and 8 PZL P.7 fighters and about 20 PZL P.37 Łoś bombers from the Bomber Brigade. So if compared to the over 3 thousand aircraft used by soviets, any spectacular achievements of the VVS in the air couldn't be gained. Of course there were exceptions and a couple of dog fights occured. But these were the isolated cases only.
Thirdly , on 16/17th September 1939 most of the Polish Army was going to be evacuated to the Romania and the units that were going to defend the Polish border consisted of weakened battalions of the Border Protection Corps (KOP) numbering 12 thousand men. However, on September 16, despite large losses, the Polish Army still numbered about 650,000 soldiers. So the soviet 465 thousand soldiers with 4800 tanks had to fight against the Polish military troops that being attacked resisted fiercely. In the case the VVS could demonstrate its force. Especially that the Polish units were also tired of the fight against the Wehrmacht. The lack of the ammo and other military equipment as the AA , for instance, facilitated the soviets in accession and occupation of the Polish eastern territory.