How does this discrepancy affect PitchF/X data, if at all?
PITCHf/x data come with a per-batter top and bottom of the strike zone indicated ("sz_bot" and "sz_top"). These are supposed to be manually added as the batter goes into his crouch, with a PITCHf/x operator marking lines at the appropriate spot on the batter. So, in theory, each pitch should have its own data that show where the top and bottom of the strike zone was for that particular pitch.
Unfortunately, theory and reality collide pretty hard on this, to the point that I (and I think everyone who looks at PITCHf/x data) mostly ignore the sz_bot and sz_top columns. For one thing, many of the measurements are ludicrous. For example, in the 2015 PITCHf/x database, I see "sz_bot" measurements -- theoretically the bottom of a batter's strike zone in feet -- that range from 2.43 down to 0.09 (ignoring the large number that are given as "0"). If you can show me a batter whose kneecaps are two and a half feet high, I will give you a nice shiny nickel. For other batters, PITCHf/x assures me that the bottom of this guy's strike zone is 1.66 feet and the top is 5.61 feet high, and that guy ranges from 1.7 feet to 4.58 feet. Because of these obviously crazy values, I have no faith in the other values, even though the great majority do seem more reasonable.
But on the other hand (and I haven't looked at this for a while, but I did play with it a year or two ago), the other PITCHf/x data strongly suggest that umpires don't pay as much attention as you'd think to a batter-specific strike zone, but have a sort of Platonic ideal of a strike zone that they only slightly adjust for outlier batters. Pedroia doesn't get the same strike zone as Ortiz, but there's not nearly as much difference between them as there should be based purely on their height.
I don't know where ESPN and so on get their on-screen strike zone from, but I suspect it's not just from PITCHf/x (because it never shows the wildly silly numbers that PITCHf/x sometimes has), and I strongly suspect that they just show a generic strike zone, and that's within an inch or so, at the top and bottom, of the zone that's called for almost every batter no matter their body shape. The TV zone is idealized anyway, since the sides are not actually square (though the called strike zone is now much closer to the rulebook zone than a few years ago -- it's become much closer to straight-sided and sharp-cornered than it used to be), so it no more than a helpful approximation to what the umpire is going to call.