Your comment makes sense and is likely the reason, I agree. The problem is the NFL, the Pats, BB, etc., don't exist without the fans. The NFL has grown in popularity of late due as much to the game itself as the opening up/marketing of events like the draft. The fans has responded by growing in number and enthusiasm.
And it's got nothing to do with the media. They only provide what we demand - access and insight. I bet most everyone that comes to this site would have enjoyed a piece or two about how fast Jones looked, or that at the camp Wilson showed why he was taken in the 2nd round. It's an opportunity missed for the Pats to reinforce their brand and generate more year round interest.
Allowing fans or the media to watch rookie camp could hardly have set back BB master plan of world domination. In season practices that include specific planning for particular teams, yes, closing them makes sense. But restricting access to the newest Patriots achieves little while bypassing another chance to fire up the nation and, through higher advertising rates and even concession sales, costs Daddy Kraft real $$ that he could, and has, used to build a winner.
The hard core fans are going to follow regardless.
The casual fan is probably following another sport right now and is not going to be pulled away by footage of unfamiliar rookies doing calisthenics or basic drills.
Advertising rates are something negotiated between the networks and the companies that by air time. The NFL already has contracts in place with multiple networks for the next ten years; a ratings increase or decrease will not change the NFL's revenue by one penny.
Revenue from licensed merchandise such as apparel sales is split equally by all 32 teams. The Patriots get the same amount of money as the Jets do from the sale of a Darrelle Revis jersey, the Raiders and Broncos make the same off a Peyton Manning jersey, etc.
As you pointed out the only potential lost revenue would be if you opened up minicamps to the public the same way teams do with training camp, making money off of food and beverages. But here's the thing: the amount of that profit is so infinitesimally small in the grand scheme of things - this is a business with annual revenues somewhere around $300,000,000 - that a couple hundred dollars made or not made off sales of hot dogs and sodas in the off-season is not going to affect the ability of this or any other team to "build a winner" one iota.
There is an oft-repeated phrase that can be seen on the walls inside Gillette:
Do Your Job. For Bill Belichick, his job is to do the best he can to build a winning team. It is
not to supply access to how the team conducts practices, no matter how much we as fans crave a glimpse of that.
There are other cases where it would certainly make more sense to use these type of activities as a P.R. mechanism to create more interest in the potential fanbase. Specifically teams that are rebuilding (e.g., the Rams) and/or teams that have trouble selling out (e.g., Tampa Bay or Jacksonville). For those clubs, opening up minicamps as much as possible would be a smart move. But for established teams like the Patriots there is really no benefit to doing so.
The games on Sunday are for the entertainment of the customer, the fans. Preparations for those events are not.