Well, I'm patiently explaining things to you like a newbie since you're asking really basic questions in this thread. I mean really basic. I suspect there's probably still some confusion on your end, or mine, with what you're calling your "Dolby preset." Dolby ProLogic II x is a Dolby processing algorithm, so it is an available "preset."
It seems if Apple TV box which costs 1/8 of the mini can play in Dolby and dts presets then the mini should be able too
It could be you still have some reading up to do with your AVR manual, or maybe I'm not fully understanding what you keep calling your Dolby and DTS presets.
The unhacked Apple TV 2 & 3 are not "bit-perfect," they output all audio at 48 kHz and you have no choice over the matter, that means when you Airplay or iTunes home share some ALAC files which (presumably) are 16 bit/44.1 the aTV 2/3 upconverts them to 16 bit/48 and passes that to your AVR. However, if your AVR is set up like mine it should still receive that as PCM, just as it would if you're playing the same exact files from the Mini--16/44.1 or 16/48 would still be PCM and the AVR processing mode for both of them would be Dolby ProLogic II x if you wanted to hear your music in all your speakers. The way most of our AVRs work is that the only way a Dolby Digital or DTS "preset" are allowed to come on is when DD or DTS encoded audio is detected. Encoded is the key word there, and PCM is different from encoded DD or DTS streams. The aTV 2 & 3 can pass through DD 5.1 with certain video files, and your AVR should light up as receiving "DD" but that's only with certain Apple approved video containers or when streaming certain Netflix titles that have DD 5.1, not playing music cds that you've imported into iTunes.
The aTV 2 and 3 doesn't support DTS so your AVR DTS light should never be lighting up wrt the aTV. Even if you Airplay a .mkv with DTS from your Mini to your aTV, say with an iPad and the Air Video app doing a live conversion, the aTV is not passing that DTS through, it's being converted to something the destination device, the aTV, supports before it gets there. What DTS audio are you playing with the aTV that you think your AVR is receiving as DTS?
In short, if your AVR is lighting up that it is receiving DD or DTS when playing music through your aTV, something's still might not be configured properly.
Personally, my ALAC from iTunes played through an aTV and output at 16/48 still sounds amazing. I tend not to use the aTV for music, and use the Mini to play everything at 16/44.1, but it isn't because of some amazing mystical difference in "soundstage" or "transparency." They sound the same, it's just more convenient for me to go through the Mini since I'm using it for everything else save Netflix.