Marie, I appreciate your attempts to help but it appears to me that you simply don't understand the scope of the problem. I realize there's a difference in perspective here (we're all guests who spend at least 75 nights a year in Marriott hotels; you're most likely sitting in an office in Salt Lake City or Bethesda wondering what the big deal is), but let me try to paint the picture for you:
Imagine if every time a guest checked in and had their credit card swiped, then they had to come have it swiped again before they could check out, sometimes by a manager or two. This is a very standard thing, providing a method of payment at check-in, and the front desk staff at all properties should easily be able to handle it. But just imagine if that process broke down somehow every single time. You'd have a lot of unhappy guests wondering why this simple process couldn't be figured out and why they had to waste so much time going to the front desk before they could check out.
That's pretty much what we're dealing with. The EEO certs are like currency that we present at check-in. If front desk associates were all as well-trained as you say, then it would be applied automatically, seamlessly, and without fail. As others have pointed out, this is true for BBs. They post immediately to a room account as a cash payment. EEOs almost never work right. It's frustrating, and turns what should be one of the biggest perks of the program into a big dissatisfier for your most loyal customers.