You are talking about value as some intrinsic quality. I'm talking about value as a belief that is subjectively assigned, and that we can infer from actions. We can all agree on the actions, and we can agree on the possible beliefs that an action can imply.

The action to not match an offer implies that the company believes the employee adds less value than their new offer. If the company believed the employee was adding more value than their new offer, they would match the offer to keep the employee.

A company isn't a single rational agent. It's made up of people performing different functions. But behaving irrationally is a categorically bad thing for the company to do, and the leadership has a fiduciary duty to prevent the company from acting irrationally or otherwise not in its own self interest.

The manager may matter here, but the leadership is supposed to be creating a management structure such that the company acts rationally to make progress towards set goals.