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Of the current formats, DTS is alone in supporting discrete back surround. DTS-ES content with a discrete back surround channel also has it matrix encoded into the left and right surround channels, for backwards compatibility. This is subtracted from the left and right surround channels upon decoding, to restore the three discrete channels.
Dolby Digital EX always uses matrix encoding and uses Dolby Pro Logic or Pro Logic II for decoding the back surround from the left and right surround channels.
As Eddy Boy mentions, matrix encoded back surround is referred to as 5.1 EX and only soundtracks with discrete back surround as 6.1. There's not much of a standard for what amps will display though. When you have separate channel input and output indicators, it is correct for the input indicator to show 5.1 channels even with EX material.
Regarding the flat, it seems that Dolby had not augmented the Dolby Digital metadata with an EX flag by the time the first Dolby Digital EX titles were released. Some older discs don't have a flag at all, even though they are EX-encoded, and requires manually switching into EX mode.
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Thank you Wayne Coyne, for thanking Jack White for the fiber-optic Jesus
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