Watching live TV indeed is the same than playing any other video file, excerpt for the fact, that this specific video file is created in "real time" while you are watching it. So it is even more weird that you could play the "timeshift" .ts video but not the recording .ts video files... If there is an issue it should have impact on both, live TV and recordings.
Quick question for @Lehmden about this:
When I play a video file on any of my clients (ripped DVD, recorded TV or any other video file), playback us pretty much flawless.
However when I play live TV or timeshifted TV on my client with wired ethernet, the playback stutters very slightly. When I play TV on my tablet over Wifi the stuttering is very noticeable. It looks like some kind of network speed issue but even my tablet play an SD movie streamed over wifi with no problems at all.
Any ideas why this stuttering only affects TV, when in fact as you say it is simply like playing any other video file?