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I do not know the source of your video file, but I can tell you that Directv verbally told me that any Directv movie files that I save to the xperia tablet will be coded to not play back on another TV (they say copyright protection). I have not confirmed this because (1) would have to purchase a Directv gizmo to save the file in the first place and (2) other discussions on this board indicate that the xperia tablet cannot handle high definition videos anyway. (BUT the xperia tablet z is still a fantastic investment at any price, because we can hold it under a water spigot!)
Not that i know an answer to your problem but when you 'Throw' a file, i believe your tablet is actually sending a copy of the video file to your Tv which your TV is then decoding itself and displaying. This is done through a standard called DNLA. If the video file has copyrite protection then i'd imagine this function wouldnt work as the TV wouldn't nesecarily have the codecs/software to decode the copy protection encryption - DNLA tends to support basic transport of non-encrypted/protected video, audio and images.
If you are mirroring to your TV it's a different matter as the tablet is essentially doing all the decoding itself and then just sending a video signal for the TV to display - the TV essentially acts as a dumb monitor.