So you yourself do not have an Outlook account, correct?
If you do, it would seem the simple way to handle this would be to set up your iPhone w/ your Exchange account, even if you only want the Calendar function (not email or contacts). That way, the appointments go directly to your Calendar for accepting/denying and any updates happen directly there as well. At least, that's how it works on my iPhone & iPad (iOS 6).
Here is an article on this:
It seems the recurring theme on these types of problems is the use of a POP email account. Something originates in corrupting or blunting the full affect of an ics event from Outlook through this method.
I guess just thinking about it, this makes some sense in that Microsoft has probably not fully developed their ActiveSync to work properly with POP accounts, especially w/in Mac OS (if you use that). It's understandable that their motivation is towards Exchange interoperability and even further, the need to support an "old" technology like POP.
Sorry I couldn't be more help, but perhaps you'll just have to continue to work around this until your migration to Exchange is complete.