You forgot that there are 13 different combinations of pairs...so it's 1326/6/13/6 = 2.83 (the diff between this and 2.67 is I rounded off the earlier value).

No I didn't. Your stated chance of any pair at table is correct - but we're talking about two specific pairs here - an AA v KK matchup.

It is the classic example of the 'how likely is that' response when you get all-in pre-flop with KK and find you are up against AA.

Incidentally last night, barely 6 hours after making the above post saying I kept donking off to made flushes I was running well at PS (with 230BB stack vs a guy witha 200BB stack) whe I hit AA in the BB. He raised in LP 3xBB, I popped him back about 13xBB and he called - flop was mono junk. Sure enough ended up running into his nut flush (a5s) for shedloads of cash..
Sometimes I need to listen to my own advice more..