From the fine article:

  the flaw would be exploitable on any machine with Java 5,
  6, or 7 enabled (whether it’s Windows 7 64-bit, Mac OS X,
  Linux, or Solaris
  [...]
  “An attacker could then install programs, view, change,
  or delete data with the privileges of a logged-on user.”

In short, you can rag on modern operating system design because whatever permissions you grant to the Java process (regardless of operating system) are the same permissions which get inherited by the exploit. If you run the Java process under sudo on Linux, then the exploit runs under sudo as well.