Prior to teaching, I spent over 25 years of my professional life working for two of the largest bank/lending organizations in the US. I agree with what the KCC guy said. Any pull granting credit is going to be a hard pull. There are other factors that can play into not as well, though. If you 'shop' credit for more than about 2 weeks prior to taking out a loan, your score will drop a little. There is 0% chance that all else being equal, a different lender would change your score in either direction.
Credit scores are also not just for loans. Your insurance rates will be lower if you have good credit, too. People with good credit are less of a risk.
The reason having too much available credit hurts your score a little is that there is a risk that after making you a loan (car, tractor, house, etc.) that you may go deeper into debt using that credit. This all comes from years of data analysis and indicators of shifts in credit worthiness.
Fyi, all lenders do not use FICO scores the same way. One of the banks I worked for used it in combination with their own proprietary model. For them, trading in a vehicle was better than cash down (again, Ceteris peribus). People who didn't trade would often still have their old car, so if money was short, they may skip payments or default. Contrary to many opinions, modern banks have no interest in repo. They will get much more by working out repayment terms.
I spent a lot of my time reading credit and investigating shady practices by dealerships. If anyone has any questions, I am happy to share my experience.