Even though it is bookable by anyone it still is a negotiated rate which is ineligble. It is supposed to be available to the group.

T&C's
Discount or negotiated rates not available to the general public, including but not limited to the following rates: membership (e.g., AAA, AARP or Saga), corporate, government, promotional, unpublished, Senior HHonors®, employee, offline wholesale/FIT, pre-paid rates which may include a voucher (including electronic vouchers), group or other specially negotiated rates.

Just my opinion but give it a go who knows it may work and since it will be a cancelable rate you have nothing to lose