I'm just about finished the ArmA campaign, and I have to add my voices to the discontent here. It does very much feel that it was rushed out the door without much thought given to the campaign or much given in the way of testing.
Mind you, I think the intention to develop a campaign of the caliber of OFP was there, and the work underway. The standalone mission 'Blood, Sweat and Tears' seems to be an outtake from the campaign - it makes reference to the camp built by engineers on the other end of the island (which, though a horrible mission, was included...). The dialogue between the SF guy and the dude in civvies seems to imply some kind of relationship. There's banter there that's too familiar to lack a backstory. Similarly the use of two named commanders (the SF guy, the Infantry guy) and the implication that they have a friendship implies more backstory too.
Further to this the method of having auxiliary missions that directly impact the main mission is a great idea, and is obviously wasted on the campaign as it stands. I can't believe the intention wasn't there to deploy it more usefully.
As to whether Codemasters would have had a positive influence on BI, it's hard to say. They can obviously demand a level of quality, but conversely the publishers can also demand substandard material be released in order to make a profit. What they may have had (this is conjecture, I don't know if publishers do this) is alpha- and beta-testing abilities beyond BIs'. This may have added to the polish that OFP had. Mind you, the quality of Red Hammer (CM) vs Resistance (BI) makes that debatable.
Given the rushed state the campaign was released in, BI obviously felt they had to push what they had out the door. The ANN news bits seem to me to be just used a glue to hold the very basics of a plot together. It wouldn't surprise me if we saw a 'rerelease' of sorts of the campaign as it was intended. The use of 'William Porter' as their everyman infantry grunt in the PR blog, and no mention of him in the game is a bit of a giveaway to this possibility. Well, here's hoping anyway, because it could be a great campaign.
(Edit: remembered BS&T mission name.)