It's not quite that simple.
Ineligible skaters can compete at the Japan Open (I presume this is why they call it 'Open'). The Japanese Federation invited skaters to compete, both eligible and ineligible. Plushenko and Buttle were invited to compete and both the Canadian and Russian Figure Skating Federations were notified of their participation but this does not grant them eligibility. The Entries section of the announcement for the event states:
The eligible skaters will be invited through respective ISU Members. The ISU Member
that the ineligible skaters formerly represented will be notified of their participation. The
list of entries is on the attached Exhibit A.
But...Plushenko has written the Russian Federation and asked for reinstatement. He was stripped of his eligibility by the ISU after passing up the World Championships and doing shows instead without consent from the Russian Federation. He had the opportunity to appeal but didn't. But now he is asking the Russian Federation to help him out in getting his eligibility back.
"Today I wrote a letter to the figure skating federation chief Alexander Gorshkov. I’m asking the ruling body to contact ISU to help me restore my amateur status. I received a personal invitation from the organizers of the tournament in Japan, which is due to take place there on October 2. I'm currently preparing for this tournament and believe that ISU will allow me to compete there."
The ISU did allow him to compete...but it didn't restore his eligibility status to compete in regular ISU competition (i.e Cup of Russia, Europeans, Worlds, etc.).
I have a hard time seeing how Plushenko gets his eligibility back. If he had appealed when he had the chance I'm near certain he would have managed to wiggle out of it but now it seems like everyone's hands are tied. If he does get his eligibility back it will have to be some 'behind-closed-door' back room deal.
And the plot thickens...