Yes, the alliance get this item. I've seen gnomes, dwarves, elves, and humans wearing them. If you think alliance characters don't start out with it, they've probably just gotten rid of it, lots of people do that. What's damned annoying is that this is the same for every other race except trolls. They all get the sleeveless, grayish black and red pattern. But we get the sleeveless crappy reddish brown. Just like the troll shaman shirt (of course that's a lot cooler). Though I believe a troll can make an orc or undead rogue alt and give their shirt to the troll looking like the other version and vise-versa.
I love this shirt, however I am alliance. I found the best way for an alliance to get this is to make an Orc rogue (which is closest to Ratchet). Walk to Ratchet from starting point. If you die, the spirit may be closer to Ratchet than you, don't be afraid to rez (you won't get sickness as a level 1).
You shouldn't die much at all if you stay on the road. Once you get to Ratchet, boat over to Booty Bay. You'll need an alliance friend or a second account, use the Auction House and put up the shirt (no deposit needed), and buy it with the other account or friend. Then get it to your char.