Pilsudski was as wary of the Germans. He was quite a nasty figure from a Russian perspective for obvious reason but still respected both in the West and in the East. That can’t be said about his followers.
In fact Stalin met with Wlad Sikorski to discuss how the Soviets could help him. Sikorski position was he wants armaments but doesn’t plan to fight in Poland and wants to fight alongside the British in Palestine instead. Stalin has taunted him with a modified phrase Lawrence of Arabia used to insult Prince Feisal. That worked and Wlad sent some guys but it didn’t work that well so he resorted to helping the Brits in Palestine. And we all know what the Brits mostly did in Palestine later in war. To expect Israel to side with official Poland is silly in light of that.