6400 is a 4 stop push. I would argue that you are not really "pushing to" an EI that high, just that you are underexposing that much, and developing and printing in a certain way to compensate for it. A true four stop push means that something that falls on a Zone IV equivalent density in the case of normal development is pushed up to a Zone VIII equivalent density with overdevelopment. Some common film/dev combos have trouble even getting to a true two stop push (in which a Zone VI fall is pushed up to a Zone VIII equivalent density). Getting a true three or four stop push is near impossible in most film/dev combinations that people use.
So, beyond a certain point, it is confusing calling it "pushing to such and such EI;" that point would be the point at which you can accurately compensate for highlight underexposure by overdeveloping. Past that point, you are basically just overdeveloping roughly in order to get a printable negative. It cannot really be said that you are "pushing to" a certain EI unless a tone that should have fallen on Zone VIII if normally exposed (but does not do so due to the underexposure caused by downrating) ends up back at Zone VIII density after development.
I think Athiril made the same point about the inaccuracy of pushing past a certain point in his last post, but I would put the point of accuracy and of true underexposure compensation for the mids and highs well below EI 6400 with Tri-X. I think that anything past or 2,000 or 2,500, and you are basically just developing a lot to help you out; you aren't attaining a true push "to" a certain EI.
I think it is much easier to discus pushing and avoid confusion if exposure and development are treated as two separate things. That means EIs should not be used in reference to development, only to exposure. Go past a certain point of underexposure/uprating, and you cannot really push "to" a certain EI. You just take desperate development and printing steps in order to salvage an underexposed negative.
I underexpose films past two stops all the time. It is necessary sometimes, and a lot can be done to dig a print out of such foul negatives, as Athiril has shown. But I don't fool myself in to thinking that I can truly achieve underexposure compensation through development when underexposing past a certain point. So I don't think of development in terms of pushing "to" any particular EI. I try to judge the light and the exposure I was forced to make, and then take development steps that will best give me a printable neg given where things have fallen with exposure. Simply calling this "pushing to" a certain EI is inaccurate and doesn't give this very involved process it the credit it deserves. It oversimplifies the thought processes and gets people thinking they can do things that they cannot.