It would be incredibly stupid for anyone to say, whatever Ottawa offers, I will beat it by a 2nd round pick. That is not how negotiations are done anywhere. Nobody in their right mind would agree to beat an unknown price. The best that would have happened is KA would say, whatever you do, talk to me before you accept anything else.
If he did, there is no guarantee BA honors that. If he didn't it's likely because the ask was still too high prior to the Ottawa offer as literally ever other suitor all dropped out of the running prior to the Ottawa deal and moved on to other deals.