in Calendar app for iOS 6, behavior of badges is inconsistent

My company has a good number of iPhones and iPads using Activesync to access our Exchange 2007 email environment. We have noticed that the behavior of "badges" in the Calendar seems inconsistent or inapporpriate.

Example: UserA has iPhone and iPad, both running iOS 6, and Outlook 2007 under Windows 7.. Both iOS devices share the same AppleID.

UserA receives a Calendar invitation. The invitation shows up on all three devices as an email. The "badge" count indicating the number of unresponded-to Calendar invitations count increments by 1 on iPad and iPhone. So far, so good.

UserA opens the invitation on the iPad and accepts or delines the invitation. The badge count decrements by one on both iPad and iPhone. Again, so far, so good.

But if UserA opens the invitation on the iPhone and accepts/declines, the badge count decrements on the iPhone, but NOT on the iPad. Doesn't make any difference how long he waits; refreshing mail on the iPad has no effect on badge count.

This (mis) behavior seems quite consistent. Do we have a setting wrong somewhere, or is this a known bug? I should say the badge counts on a number of my iPhone and iPad applications behave in, let's say, an unusual or uninformative manner. But this behavior in an enterprise environment is driving my CIO crazy.