Would it have hurt too tell the truth about Poland?

You're quite right, and the omission of this little tidbit is one of the things that makes Mission to Moscow so outrageous in its lies and distortions. If you look at the map they show -- of Poland literally being burned up in the German invasion, and later when it shows the German assault on the USSR -- not only is there no mention of the Soviet invasion, but in the second shot the Germans are indicated as already occupying all of Poland, right to the old Soviet border. And, of course, there is no mention of the Soviets' annexation of the Baltic States.

I disagree, though, that Churchill is seen as a "dope". Not at all: he comes across as one of the few far-sighted people on the scene at that time. In fact, this is one of the few areas where the film is more or less accurate. Throughout 1938 (Munich) and 1939, Churchill had been a vociferous advocate of Britain and France forming an alliance with Russia against Hitler. But Chamberlain and his circle hated the Bolsheviks and deluded themselves into believing that Poland was a stronger military power than the Soviet Union -- hence, their guarantee to Poland in April, 1939. As a sop to public opinion, the British and French did send a delegation to Moscow in June and conducted half-hearted negotiations with the Russians, who quickly realized (correctly) they were not serious. It was only after months of this Anglo-French foot-dragging that the Russians moved to make a pact with Germany, both for their own security against attack (at least for a time) and because Hitler offered Stalin territory, which Britain and France could not do (although they had had no such qualms about offering Hitler territory the year before at Munich). Churchill was vehemently anti-Communist but understood that the only chance to defeat the more imminent threat from Germany was by making a pact with the USSR amd sticking to it. The ignorance of, and antipathy toward the Soviet Union by, Chamberlain and his sycophants was one of the key elements in helping bring on the Second World War. (This was also seen at Munich, where the USSR was excluded even though it had a treaty of defense with Czechoslovakia and should have been consulted -- but then, of course, the Czechs themselves were excluded at Munich.)

Churchill later did denounce Stalin for his actions in Poland (as well as in the Baltics and Finland), but that still didn't stop him from allying Britain with Russia after the German invasion in June 1941. Where Germany was concerned Churchill was always a realist, and correct.

The truth about Poland? You mean about how Poland had opportunistically stolen a great amount of Soviet land with the motive of expanding Poland's borders as far east as possible so as to build a new Polish empire? How most of the people of "Eastern Poland" weren't Poles but were Ukrainians, Byelorussians and Lithuanians who were second-class citizens under Polish rule? Funny how no one ever mentions that part. Funny how it's ok for Poland to steal Soviet land (openly declaring an intention to expand as far as possible), but it's not ok for the Soviet Union to take it back.

"Killing is murder unless it is done in large numbers to the sound of trumpets."
- Voltaire

The division of eastern Europe was in a secret codicil to the pact. This was not discovered until German records were investigated after the war.
At the time, Stalin justified his invasion of Poland as a measure to prevent Germany from occupying all of it, and I guess the West believed him.