I just joined a Galloway training group this weekend, and saw the man himself give a seminar last weekend.
For 10 min mile, yes, you do 3:1. I am in the 13 min group, so we do 1:1.
It isn't so much for making you faster (although he claims it does), as to finish feeling great, and train injury-free. Because you are giving your "running muscles" rest, you can go further and maintain your pace for longer while not causing as much muscle fatigue (and therefore damage).
He also has a lot of other advice, like training 2 min slower than your race day pace. He has a "magic mile" formula to determine 5K, 10K, half, marathon pace. The magic mile is your 1-mile best, i.e. how fast you can go, pushing yourself, for 1 mile.
It was actually sort of freaky... I didn't know much about this program before the Princess, as I trained using a program that 3DisneyKids, who posted above, gave a bunch of us that were training for the Princess (thanks E!!). However, I used his calculator a month or two after the race, having stumbled upon his website. My 5K pace, which was my short run during the week, almost exactly predicted my half finish time using his formula.
I did not really use his methodology for the Princess half, because, well, I mostly walked it.
I ran some, but not in any predictable intervals. I was just happy to finish well under the 3.5 hour sweeper time!!