I can imagine that they had only plans if Hitler had had more success and that those two cities werent the only possible targets and that they had no real intention behind it, but the Channel decided to use this information because its the Region they are sending to?
If someone doesnt know why these cities are relevant: The BASF (now) one of the biggest chemical companys is based there. They also lie directly at the river rhine.
I have gone over all documents I have found regarding targeting decisions and philosophy for the atomic bombs (there are fewer than one might think), and I have never seen those cities mentioned. This post goes into detail on what little there is regarding Allied plans to use the bomb on Germany — basically, it was never taken up systematically as an idea, because of the timing of the bomb project, though Roosevelt did express some interest around the very end of 1944, but the bomb wasn't ready and wouldn't be for six months.
I would note also that since Mannheim had been heavily bombed since 1940 (and was 64% destroyed by the end of the war), it would not have been a likely candidate under the targeting guidelines developed for Japan, which favored un-bombed, "virgin" cities in order to showcase the destructive power of the bombs.
This is probably a question for /u/restricteddata, but since he's asleep, I'll take a stab at it.
I haven't seen anything suggesting a target in Germany. In the May 1995 issue of the Bulletin of the Atomic Scientists, Arjun Makhijani has an interesting article entitled "'Always' the target?"
In it, Makhijani examines the first known discussion of weapon targeting, which took place in a May 5, 1943 meeting of the Manhattan Project's military policy committee. According to Groves' summary of that meeting:
"The point of use of the first bomb was discussed and the general view appeared to be that its best point of use would be on a Japanese fleet concentration in the harbor of Truk [just north of New Guinea, and a dangerous place for Americans in 1943]. General Styer suggested Tokyo, but it was pointed out that the bomb should be used where, if it failed to go off, it would land in water of sufficient depth to prevent easy salvage. The Japanese were selected as they would not be so apt to secure knowledge from it as would the Germans."
As Makhijani explains in the article, the scientists working on the Manhattan Project had a different view. Almost to a man, they believed that the bomb would be used on Germany first.
The first really serious discussions of targeting didn't take place until spring/summer 1945, with the creation of the Targeting Committee, and at that point, Germany's position was already clear and there was no thought given to any target other than in Japan.
I don't know where your documentary got the idea of Ludwigshafen or Mannheim, but I'd be interested to know.