The concept of the "backward" American (Canadian too, I suppose
) flag is that usually on the right hand side/shoulder, its meant to signify going forward/running into battle (as if you're carrying a flag pole) with the flag streaming behind you, as opposed to running away.
I am sure Nike's taken that similar type of attitude with their logo.
Different when you're turning around a letter, obviously.
That said, I also see ones of that style on NHL.com have the flag patches, not the "C", and look to be a darker red.
http://shop.canada.nhl.com/largeImag...20377426dt.jpg