This is untrue, and the historic record of this is untrue, put into records long after FDR left the office. While FDR himself was a big proponent of US joining

This is untrue, and the historic record of this is untrue, put into records long after FDR left the office. While FDR himself was a big proponent of US joining the League of Nations, he himself was fully conscious that him inviting Stalin into the UN would make it pointless, and useless. His fear was exactly that UN will not be toothless, and US position as the biggest post-war power will be hampered by an international body, or it being dragged into conflicts by Europeans, so Stalin was his way to put a deadweight on UN's neck from the beginning. UN was an organisation which even originally rejected many quite decent democratic nations for minor flaws, and principally, opposition from major powers. Heck, even Germany was only allowed to join in seventies. So, no illusions about that. Maybe, his another concern was that he would've never be allowed to join the UN by the congress, unless he were to provide the republicans with assurance that the body is useless. That's my own theory I developed when reading on FDR in high school.