Neither the players or owners control the cost of ticket prices. The market dictates the price of tickets. The players could play for $1, but if the market dictates fans will pay $39 for an upper level seat, then the seat will cost $39.
Supply and demand.
Supply and demand would actually exist if it were within a free market vacuum. However, it is pretty clear that the free market doesn't exist in this case (or just about any other if you want to look down the barrel of this POVs logical and practical end). If it WERE an actual free market, then there would be alternatives to the NFL and there would be competing unions for said services.
That doesn't exist, so the usual maxims of supply and demand do not translate 1 for 1 as you suggest. If the NFLPA is allowed to bully the NFL into an unsustainable business model, then the only way to recoup costs is to pass it on to the customers.
This is precisely what happened in ATL when Arthur Blank took a HUGE hit at the ticket booth to get people in the stands his first year. He wanted to keep doing it, but he would have been out of business LONG ago if he continued on that course.
This isn't the ivory tower of academia here... this is the real world. The owners in the NFL haven't gotten to where they've gotten without an understanding of how the real business world works. They are simply trying to apply their practical real world acumen to the NFL business model in a modified fashion to see the league's continued success. If that process is hijacked by a legal dispute by the employees, the NFL will die a faster death than what Detroit has been rescued from... unless of course, we compell the American public to subsidize the NFL. God knows what will happen then.