Run DiskWarrior from USB

I want to be able to rebuild the directories of my Mac Air (which is still fully functional) running DiskWarrior from a USB Key, but I have one issue I can’t fix.
I have installed Moutain Lion on a properly formatted USB Key. I restarted my Mac (on which I have Mountain Lion) pressing the option Key,
and booted from the USB drive. I then copied the DiskWarrior .dmg file from my Mac to my Desktop, and I have installed DiskWarrior on my USB drive (under utilities, in the app folder). Then I launched Diskwarrior and I selected my Mac’s hard drive, and DiskWarrior tells me “Directory cannot be rebuilt, DiskWarrior resides on this disk”.
I don’t understand why this happens (since I am running DiskWarrior on the USB key), nor do I know how to fix it…any ideas?

PS
Notice that I am NOT also told “The Directory Cannot Be Rebuilt Because This Is A StartUp Disk” (I get this message (plus the above one), only if I try to run DiskWarrior when booting from my Mac)

 

yes, but...problem solved!

I was booting from the USB (yes, I am sure), yet your comment was helpful in making me realise my mistake:
I had added the Mac’s app folder (instead of the USB’s) onto the Dock of the USB’s User Desktop; so I had actually installed DW (DiskWarrior) on the Mac's app folder, so even if I was actually booting from the USB I was accessing an app which was on the Mac’s HD.
Because of this, when booting from the USB and selecting the Mac’s HD, DW was telling me that “Directory cannot be rebuilt, DiskWarrior resides on this disk”, yet it was not telling me “The Directory Cannot Be Rebuilt Because This Is A StartUp Disk”, since truly I was booting from the USB drive.

Now I moved DW on the USB app folder, and running it from there I can finally select my Mac's HD.

Thanks for your help, cheers