I think if we bring abstentions into the equation, Alan's point seems to be stronger, rather than weaker.
We have a Board of 16 voting directors. A 2/3 majority is 11 (11/16 = 68.75%). (By contrast, a simple majority is 9 (50%+1).)
Thus 11 Board members must vote to reject an item of GAC Advice under the proposed Bylaw. If 10 (62.5%) (or fewer) Board members vote to reject, Advice is (presumably) "accepted." Under this scenario, with no abstentions, 6 members (37.5%) have voted to accept (or, at least, not to reject) GAC Advice; thus, ICANN must abide by advice that supported by only 6 out of 16 Directors. And that is the best case scenario when a vote to reject falls just short.
Under this same scenario, with 10 votes to reject, and 5 members vote to accept the advice and 1 abstains, we now have 31.25% of the Board in favor of the advice we must all abide by. If there are 2 abstentions and 4 in favor, the percentage in support drops to 25% (and then to 18.75%, 12.5%, 6.25% and 0% as abstentions increase).
If only 9 members vote to reject (a simple majority) and none abstain, then the accepted advice is supported by at most 43.75 of the Board. If one abstains, the percent in support is 37.5% and so forth.
If only 8 members vote to reject, at best 50% of the Board supports the advice. If one abstains, that drops to 43.75% and so forth.
If only 7 members vote to reject, we finally get to the point where the majority of the Board supports the Advice (best case scenario, assuming no abstentions). With one abstention, that drops to 50% and so forth.
Greg