Definitely what have you got yourself into? They sound like one of my ex-employers. :)
Customer or competitor - to think that they won't do anything is off the top mark of the naivety scale. And are they really prepared to risk finding out whether co B will take any action or not?
They sound a bit dismissive that they are not aware what a website could do for them. They should be investing the time/money to come up with something that potential customers will love and will equally knock the competition's socks off.
HTH
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