Churchill once said, "The truth should always go accompanied by a bodyguard of lies".
Knowing that the enemy would always be able to see what was happening, it was crucial to give the enemy false information concerning things that were not happening.
We did the same to the Germans on D-Day. But to say FDR knew that PH was the target is to fall into that conspiracy black hole where FDR needed the US to be attacked to get out of the Depression. This “story” has been going around for years.