Agreed, I also have no idea how the tv deals with varying frame rates, although my guess would be that it doesn't and there is no conversion. After all the tv has to cope with frame rates other than 30/25/24 and would need to work to a whole bunch of conversion algorithms covering the eventuality of not only many possible frame rates but also two different refresh rates.
One way of coping with various frame rates would be to play them frame for frame in the same way that 24 fps video is played on a PAL system, resulting in the media being speeded up or slowed down. Whilst this is essentially unnoticeable for 24 fps playback on PAL, it would certainly be noticeable for video encoded at 12 fps for example, since 12 fps video suffers no such speeding up on the tv, it's likely safe to assume the tv does not employ this technique.
Simply playing (for example) 24 fps content at 25 fps will result in tearing as the image changes in the middle of a single scan, again I don't particularly see any evidence of this on my tv's but it may be slight and unnoticeable and indeed may depend on the tv itself.
Even if we could see the motion judder, it would be quite difficult to determine why it occurs, indeed as you point out it may well be an issue introduced in encoding or even one of peak data rates, not being able to see the OP's problem makes it even more difficult, but a restart of the tv may help in some cases.