And they are not saying you are asking them to lower it permanently. They just won't lower it at all, even temporarily, since you already have the lowest available non-promotional APR. In other words, because you already have a great non-promo APR, they are not going to give you a 0% promo.
It makes sense from their perspective. You have 10.99% APR because your credit is good and they figure the only reason you are asking for a temp 0% is so you can carry a balance for that period and then pay it off. In other words, they know you are not likely to step in it and actually pay them interest later, which is what 0% promo rates are meant to do, so they are not willing to let you earn interest on your bank balance at their expense. 
Yfan pretty much summed it up. It wouldn't be convenient or a good business decision for them to give you a promotional 0% APR because you have their lowest rate and good credit. They know how us MyFICOers work. Haha.
