According to Livingstone's letter, the £600 million will come from the
taxpayer and go to the Reuben brothers (or the company in which they
have an interest).

If, by "OA", you mean the Olympic Association, that does not seem to be
the case, according to the letter from which I have quoted.

I have no idea who the Reuben brothers are, but if they are the sort of
money-making businessmen that Livingstone is accusing them of being,
then this ought to have been known earlier, and it is negligent not to
have taken into account their effective veto BEFORE the bid was made.
To answer the question you ask, I (who have no interest in sport or the
Olympics whatsoever) too would be "uncooperative" with Livingstone if
that were a way to make money!

Marc.