True, but it's not a lot of money to an organization with a ~200 million dollar payroll.
250k is less than 1%. Thats like a company giving an employee with a 50k salary a raise of $70.
Well, if the company has 1 employee, meaning their total payroll is 50K, 1% is still $500. Other than those 2 details, you nailed your analogy.
And yes, MAT likely doesn't have a future with the Nats. I think he's already trade bait, and it's easier to trade him to a cost-saving team looking for a cheap OF if he makes 250K less. I've helped on some arbitration-eligible players for a MLB agent, and teams do NOT want to actually go to arbirtration unless they see no future with a player. It gets ugly because you essentially argue why the player isn't worth that amount and point out all their flaws.