Ali and on-speed, that was the one I had to think about for a while as well, but I'm reasonably sure of my facts (as they relate to my specific aircraft type anyway) because I've just had a chat with a bloke who recently joined Cathay from my company, and he got asked this very thing in his interview and explained it this way.
Picture yourself approaching V1 and taking off in a max crosswind from the right. The aircraft is wishing to yaw into wind, to the right, and therefore (in my aircraft anyway) you are holding a hefty boot full of left rudder to keep it straight on the runway.
Right hand (upwind) engine now fails between V1 and VR.
The aircraft now wants to yaw even harder to the right due to the engine failure. What you need to do, is apply further left rudder to counteract the yaw, but you can't, because you haven't got any more left rudder available, you've already used up 90% of your available rudder travel keeping the aircraft straight in the crosswind. The only place you can go from here, is into the grass on the right hand side.
Whereas if you lose the left hand (downwind) engine, then the yaw due to the failure will be towards the left. Since you're holding a bunch of left rudder anyway you need to reduce / remove the left rudder input, but you've still got all the available right rudder after that, and the yaw due to the crosswind will actually be helping you keep it straight in this situation.
This guy banging on in the book about 'restoring moments on the fuselage' sounds like a collossal pile of codswallop to me, I've worked at one or two different places as a multi engine instructor in my time and I've certainly never run into any other training notes that make any reference to such a thing.
Maybe it's different in jets with immensely long fuselages or something, but I'm definitely going to stick with what I know I can explain
