"...That if I didn't like my financial aid package, I could negotiate for a better one. Is this true?"
This is a question that I've only heard a couple times. More often, instead of asking that question, the student or the parent just tries to negotiate. Unfortunately, it's not that simple. Financial aid isn't like haggling in a pawn shop for a good price on a night stand that has some scratches and duct tape.
Financial aid amounts are determined by strict sets of guidelines given to the financial aid offices by the federal government. There is very little wiggle room as far as if the financial aid administrator is able to change the amounts of aid a student can receive.
The same goes for interest rates. The federal government determines the interest rates for their student loans, and there is nothing a school can do to change those. I once had a parent try to talk me into matching the Unsubsidized loan's interest rate in the PLUS loan. It's not possible. They are set amounts. Unlike home loans, car loans, and personal loans, there is no qualifying for a better interest rate since there is no credit taken into account. It is what it is.
When you are applying for a school, the school will try to give you the best financial aid package that they can. Remember that schools have different rules and different sources of financial aid, but also remember that your entry to the school will have them getting you the best package available to you for that school. They won't give you a bad one on purpose for two reasons: 1. they want to give you the best so you'll attend their school, and 2. the best they can give you is what their job is. They are only packaging you for what you qualify for that school.
It may not be what you want, but it's their best offer. Your only option is to check other school's financial aid packages. Some schools, you will find, will have different amounts. The other thing you have to consider is the degree you are going for and what you want to invest in it.