I have never thought traveling back or forward in time was a reasonable explanation, (I guess to some there is no reasonable explanation) but the cases I have read have more of an observer feel to them rather than a person actually being physically in another time, if they were surely the time paradox would apply, and your position in space and time (as mentioned earlier in the thread)
So to me it's got to be another reality that someone is living in and we get a glimpse of it, and only some people (which is very similar to much Fortean phenomena)