The original video as recorded by EyeTV is 1440x1080 *pixels* with a picture aspect ratio producing a display size of 1920x1080.
Load it into HandBrake and select the Apple Tv 2 preset and you see:
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Picture Size: Source: 1440x1080, Output: 1280x960, Anamorphic: 1706x960 Loose, Modulus: 16
I didn't actually run the encode as I don't have an AppleTV2 (yet) to play it on anyway, i was just looking; but my guess is, it and the iPad would refuse to play it as even in terms of pixels it's > 720p.
My workaround would be to open Picture Settings and scale down until the vertical resolution is 720, at which point the display width is also 1280. It's an easy workaround which I expect would work but I presume you may want to make the preset behave that way anyway?
As an aside, it might be nice, even obvious as we're downscaling in both dimensions, to go from 1440x1080 pixels anamorphic to 1280x720 pixels non-anamorphic, but after a quick play that doesn't seem to be as straightforward as one might have expected.