Just got iPhone 4s and have the exact same problem. These are all Exchange invites done by my assistant from her Outlook. I already exchanged to a new unit and the problem persists. What's more frustrating is that some invites work and some dont. Most do exactly as you describe. No option to accept/decline and go straight to my calendar while the invite on my Outlook sitll shows as unaccepted. The same problem exists if I open the actual iphone calendar notification or the attachment on the email sent by Exchange. It is extremely frustrating.
I have tried everything to try to analyze what is causing this and cant seem to get to the bottom of it and cannot explain the randomness of the problem. I am so dissapointed that iPhone and all its hype cant seem to get plain business functionality as good as Blackberry.
Would love to hear comments on this.