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I don't like bringing real physics or logic into discussions of fictional anime because the 'real' physics people start bringing up in order to explain stuff like time travel or alternate universes is crap.
On the issue of relative motion that's been brought up. The problem, you see, with applying that as an obstacle for some sort of time machine is that you are also assuming that space 'exists' in anything more than a local sense. Why should any one reference frame be preferable to another? If God picks the frame of 48 light years to the southwest of the Milky way for the conduction of my little time travel experiment, why can't I (equally objectively) pick the frame of the streetlamp anchored to the earth as my 'coordinates'? It's all the same.
But then again, that's also the problem with portal-based or teleporting time travel in the first place. Time doesn't exist in anything more than a local sense either. To be clear, that means that 'past' and 'future' don't exist either, in any sense beyond Laplace's claim that, if a sufficiently powerful intellect knew the position and velocity of every particle at a given time, it could calculate the position and velocity of any particle at any other time.
Time travel in Haruhi Suzumiya is dealt with by assuming the existance of a 'picturebook', to serve as a record and target point of various instances of 'past' and 'future'. This allows 'travel' by providing actual destinations. Scientifically, though, there is no reason for the existance of any such 'cosmic history', and any attempts to reconcile those fictional tropes with 'actual physics' are futile wastes of time.
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