you've got a pretty good handle on this.
a DTS capable system will be able to play back any source in whatever format in which it's been recorded. Whatever receiver you buy that can decode DTS, which is all of them, will be able to play Dolby Digital, stereo or mono as well. But, they won't play back in DTS. That's like having a HD TV and expecting a rerun of "The Honeymooners" to show in full screen HD in color and with DTS sound.
Your receiver will play back your source in whatever scheme it was recorded In, be it DTS, Dolby Digital, Stereo or even plain old mono so yes, to play back in DTS, the source must have been encoded with DTS initially.
Most receivers have an "auto" function which will play back your source in the best format available, be it DTS, DD or stereo, which will probably show up as either DPL or Neo, depending on how you set your receiver.
As far as I know, about the only recordings consistently recorded with DTS are Blu-rays, and that's not even a 100% certainty. DVD's and some streaming services like Netflix, amazon, and probably others will top out at plain old Dolby Digital, which doesn't suck. Your music services like Spotify, Pandora, and Slacker will top out with two channel stereo.
So, to sum it up while DTS is nice and a preferred method, I think only Blu-ray, and maybe a very few DVD's offer it,
to realize the benefit of these newer hi-glitz DD/DTS formats, you'll need to feed your source directly to your receiver with a HDMI cable. Digital coax and fibre optic will only allow your basic DTS or Dolby digital at best,