After experiencing the very same problem and symptoms, I was able to gain access to the Apple Developer Forum thread mentioned here
The upshot of the Apple thread is that you must have a valid Intermediate Certificate installed on the server. It is not enough to have only the server certificate installed.
I have tested this with Mac OS X 10.6 Server. I installed the server certificate and while desktop browsers were able to stream a video over HTTPS, iOS devices (iPhone and iPad) both gave the "This movie could not be played" error.
Installing the Intermediate Certificate fixed the problem.
Other devices, like Android phones and tablets, and RIM PowerBook (via Flash) had no problems playing the video without the Intermediate Certificate. I suspect it is a case of iOS being overzealous with its security, a "Feature" if not a bug ;-)
I'm not a PKI expert, so I cannot tell you why this works. Perhaps another contributor can explain the PKI voodoo behind this.
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