Hmm, interesting. At NM, you get "double points" in the sense that you earn one Amex MR point and one InCircle point for every dollar you spend at NM/BG on you REGISTERED Amex Platinum/Centurion.

Here's how InCircle double or bonus point events work at NM. On a 1000 point bonus day, if you make a $500 purchase at NM on your NM charge card, you will earn 500+1000=1500 InCircle points. If you put that $500 purchase on your Platinum/Centurion card, you do not earn the 1000 point InCircle bonus, so you'll earn 500 InCircle points and 500 Amex MR points.

The solution is to use both cards. On normal days I use my Platinum at NM. On bonus days I use my NM charge card.

From the page you listed, it looks like double point events work at BG. Very odd. I spoke to InCircle several weeks ago and they told me that bonus points never work with Amex, but maybe she was referring only to NM, and BG is different. I'll call InCircle next week and ask for clarification. If the Amex worked during those event, that would be great, you'd be earning double InCircle points AND MR points!