This is followed by more threats:

There’s a misconception that accepting a counteroffer only hurts the company you are turning down – not true. Besides forever ruining your chances with the newer company, you have also left the door open for this company to share their history of you with others in your professional field. Do not be so naïve to think these things do not spread. You will find that the industry is surprisingly small and that a name can spread very quickly.

Is BINK threatening to drag your name through the mud for making the best decision for yourself – likely the reason you started to look for possible opportunities? It is unfortunate that predatory recruiting companies like BINC use fear mongering to make money off of you. In the end you are responsible for your employment decisions. Perhaps BINC hasn’t considered the idea that companies exist out there that want to retain valuable staff through flexibility of pay, environment, and position.