I think D'Z's theory is sound. I thought of it but thought it was flawed since they didn't just switch the belt back to Orton and HHH then fired Armstrong completely. But looking at it deeper, the plan could have been that HHH told Armstrong to call the match fair because he WANTS Orton to win cleanly as a way of showing everyone that Orton does genuinely deserve to be the face of the company over Bryan. But then he also tells Armstrong that if at any point it seems like Bryan could win and Orton might not recover from a three count (a submission loss is a different story), do a fast count and then try and say that he conspired with Bryan to cheat to win the belt. That would give HHH enough incentive to take the belt from Bryan and hold it up.
I still would question why not just switch the title back to Orton BUT as I mentioned before, maybe HHH genuinely wants Orton to beat Bryan fair and square to prove to everyone he deserves to be poster boy of the company over Bryan. That could also provide a good reason why HHH and Steph chewed Orton out so much backstage and asked him to bring back his amoral Viper persona, because they legitimately know Bryan had Orton defeated the night before and Orton needs to be more aggressive to ensure that doesn't happen again.
As for Armstrong being fired, that could all be apart of the cover up to further convince skeptical people that HHH wasn't involved. Maybe Armstrong will show up with his kids next week or something and plead to HHH/Steph on-screen to rehire him because he's got a family to feed. And HHH does, thus convincing people that he didn't plot anything out with Armstrong because he fired him, although he still ends up getting his job back anyway. (OR since HHH says that he offered Armstrong a huge severance pay, maybe Armstrong happily takes his permanent unemployment to help sell the story.)
But yeah, seems a bit too complex than WWE usually likes to go (even though it's still fairly easy to keep up with for me.)