... redacted - see above ...
Not to get too philosophical here, but I tend to think what a team offers a player (in their final offer) is the definition of what they think the player is wroth to them.
That's true as afar as it goes: teams only evaluate players based on their value to the team. With really good players the value is far beyond what the team can offer, so price tends to match market value. For the role players and reserve guys, since teams have a lot more ability to pay what they want, I'm guessing the valuation focuses on value to club.
In other words, market value is by definition what a player can make as a FA. But the team is not bound to pay that, and can value a player with its own approach. This doesn't mean the team doesn't see that difference "we know the market for Posey is X, but his value here is <X so we're not going to match, wish him all the best, etc."