It's not logical to think that the government deliberately mistranslated the tape because it would be too easy for anyone who speaks the language to show them to be lying.
Having transcribed from audio tapes on a regular basis for over a decade, I can tell you that a transcript done in haste will have some inaccuracies. Also you have to understand that different people will hear minor things differently, no matter how much time is available to transcribe it.
This is just more nonsense from people who make money from "exposing scandals." To report a story in a sensational light is more profitable than to report that everything is just fine.
I know that 200,000 Germans held a candlelight vigil in Berlin a couple of days after the attacks in support of the U.S. Pictures were posted here on FR.
That's more than turned out here in the U.S. If you are going to suggest that Germans hate the U.S. you can pick a different fellow to foist that assertion upon.