Now THAT is slick! I, too, watched the video, and had the same question as sandyl- I assume at some point you'd pinch the 1/4" seams together on the back and sew 'em up? I've got a Lone Star PIW, and this would make the process SO easy!
I have another question: How much bulk do you have in those first sections where she DIDN'T cut off the triangle piece underneath? Why did she not clip off that one where she clipped out the bulk from under the others in the row?
Is your quilt "stiff" with that extra layer of interfacing underneath?