The part about not paying cash is the fact that you want your salesperson to think he'll have to overcome securing financing for you. Banks only advance a certain percentage based on dealer invoice. Say 13k on a 10k car. Thats an advance of 3k. But salesguy wants to sell it to you for 15k and you don't have the 2k difference in down payment then the deal is squashed or he'll have to lower his price.
Its highly likely he won't shoot for the homerun unless you're cash buying because no one wants to come down after a deal is done, that leaves a bad taste in peoples mouths. Most people would be "well it why didn't you come down in the first place". If they try and sell you something thats too expense the salesperson is stuck having to ask you for some big money down to close the gap. If you cash buy there is no gap to close all he has to do is get you to make the purchase and if you like what he has he can charge you an arm an leg for it without having to overcome a bank or the worry of a downpayment.
Everyone wants little to no down so a salesperson will write skinny to medium size deals to keep from having issues. Less issues = quicker close.
Thats why they ask you if you have a downpayment. They can bump the price without a bank getting in the way.
mark it
You need financing and you probably need 0 down. Then go from there.