Man, the more we discuss that failed Radulov outcome, the more scenarios are brought up.
I have followed this from the beginning and I don't remember this being the reason for Radulov taking the Dallas offer. Maybe you have a source I haven't seen, so I can't really confirm your version.
I distinctly recall that Bergevin had Radulov to himself, there was no other suitor after he chose to become a UFA. Bergevin sensing that he had the upper hand, made a take it or leave it offer. Radulov was considering it but didn't accept it. Bergevin decided to play hardball and told Radulov that he was withdrawing the offer. It is only when Bergevin created a vacuum by withdrawing that Nill swooped in and offered Radulov what he wanted.
It was reported that Radulov only having the Dallas offer on the table and nothing else, made the decision to accept it and gave Nill a verbal OK. Bergevin thereafter circled back and made the same offer as Dallas to the Radulov camp but since Radulov had already given his word to Nill, he rejected Bergevin. It is important to note that Bergevin's offer was the same as Dallas, again as confirmed by reports at the time. Bergevin shot himself in the foot by withdrawing his offer in order to coerce Radulov and had not anticipated that some other team might actually give Radulov what he was looking for.
That's what I remember distinctly from what transpired.