Byrd hired Eugene Parker for a reason. He didn't hire Parker to 'get a deal done', he hired this specific agent to become the highest paid player at his position.
Unfortunately, Byrd doesn't have very many cards other than the one Parker is trumpeting that he was 'underpaid'. If the Bills franchise him for the next two years, they get two years at a rate lower than what Byrd wants and can work towards replacing him. As Parker so helpfully notes every time he opens his mouth, Byrd was 'underpaid' and while that annual salary is nice, he will be fined for missing camp and then not get paid until week 10. That's a lot of money to give up over the next two years to risk injury and a down season to get to Parker's "megadeal'.