That just means the Widmore Corporation has been "involved" with the island. So was the Hanso Foundation and Suns fathers company, Paik Heavy Industries...It doesn't mean Charles Widmore owned it, or the Darma Initiative. Although Charles seemed to think it was all his, I think it involved a lot of people. Probably all the people that Sayid is going around killing.

Actually, the "logo on the folder" discussion is on another thread.