By exploit standards, that's not especially hard. I don't think there's really anything blocking accessing it at all if an NTFS volume is mounted on a typical desktop Linux distro, as it's just NTFS permissions blocking it, and they're not typically obeyed by Linux in the first place.

In the face of your edit, I see that you've misunderstood the exploit. You need write access to the System Volume Information directory of your own USB stick, not anything on the target machine. It's much easier to get access to things on a computer than it is to get access on one particular computer, and this exploit lets you jump from one to the other.