I disagree with your conclusion because it is not based in facts.
There is no bargaining with a school like U Penn. In some very rare circumstances, you can present them with facts which were not in evidence when you applied- breadwinner lost a job, heavy medical expenses. And they may reconsider. Or- in even MORE rare circumstances, you can show them that Cornell or Yale has admitted you with a more generous package (although they are more likely to tell you to go to Cornell or Yale if they are cheaper).
You need to run the numbers with YOUR facts- salary, assets, number of people in the family, etc. What someone else gets or doesn’t get isn’t relevant for YOU.
But bargain? Good luck.