Brits are completely aware that Americans spell things differently, personally I don't feel it needs pointing out. Makes it look like the writer thinks Jack is wrong!
Googling "BBC using sic for American spelling" brought me to your comment, and looking at the other results it doesn't look like they do it all the time. Seems silly to have done it at all!
I wager it get's edited away before the end of the day.
I'd either ignore it, or just change the quote to British English, I assume that's not going too far.
edit: apparently it is going too far. Quoting across the Atlantic is a common issue faced by writers, and it seems the consensus is that you always just quote letter-for-letter.
If he tweets "I realize [sic] this is a silly question", how would they quote it?
You mean "you weren't joking"