Doesn't Ben say something to Widmore about "your rock is nice this time of year"? Which I took to mean either the Island or the Black Rock. And if Widmore is an ancient as we suspect he might be, then the Black Rock could literally be 'his', and that's why he refers to Ben as "boy" (because Ben is so much younger than he...centuries?...and because he considers Ben an upstart who 'stole everything from' him.)