Donkey Alert! Please Advise

[oaktoon]

final two tables in a live tourney-- $200 buy in. Prize structure is either a) winner take all/winner wins seat at WSOP main event or b) $4,000 first prize, followed by usual ratio of 2nd thru 9th. Basically it's a question of whether the final table is willing to chop at any point, or whether the chip leader(s) decide to go for broke. That element may play into the hand described below.

Total chips: 480,000

18 players left, so M is approx. 26,500.

Hero has 10,100 in cutoff position.

Blinds are 700-1400

UTG with about 15000 chips calls preflop

Mp+1 with approx. 20,000 raises to 5,200.

Hero goes all-in with JJ.

BB with 35,000 chips goes over the top.

MP folds.

BB turns over K9 suited.

Flop is K9x; adds insult to injury with 9 on turn for fullhouse.

MP had AJs-- no ace hits so hero would have doubled up plus if it was heads-up the other way.

Question: did BB make a smart move given the likelihood that he could isolate and the value of a huge chip stack in the ultimate negotiations about the prize? Or was K-9 vs. raise/reraise where certainly a high A hand and a strong pair were the likeliest scenarios a hand that should have been mucked?

(not too ticked of, mind you, since I had just hit a miracle 80 to 1 shot when my AK vs. JJ and a Jack on the flop had hit runner-runner Q and 10 just ten minutes earlier?