Complaint sub-issue: Credit inquiries on your report that you don't recognize

This is crazy. Went online to Carvana around XX/XX/XXXX this year searching for cars. I had received a pre approved offer for a {$1000.00} down payment, so I was just checking out cars and prices. Decided to fill out the info for the car I head been checking out. Had updated my contact info, verification, uploaded license, and was trying to enter my bank into when I was took to a screen with documents to initial and look over. I had just begun to read the fine print when I got a notification that my credit had been pulled. I hadn't even submitted any paperwork, nor asked to have my credit filed pulled! Furthermore, I wasn't going to go for the deal with the contract they were writing up due to the interest rate that had doubled the price of the car, then some. In other words, I hadn't signed anything, nor agreed to any credit checks. I immediately called Carvana to find out what was going on and ran into XXXX. I was very polite in asking him about the credit check, and the fact that I was never asked if it was ok to have them check my credit, nor did I sign any agreements, since there were none online to sign. He replied that there was an online agreement, that I just " didn't see it. '' I asked him to go online and guide me too that agreement. He agreed to do so, but after a few seconds, told me that I had already signed the paper work, and that my " signature '' covered it up so that it was no longer there. I had never heard of anything like that before in my entire life, and plus, I hadn't signed anything so I told him as much. We went back and forth as to why my credit was checked without my authorization, with him making up several different excuses, one being that they were a " different kind of car company '' and another that I had already finished the application, which I hadn't. That still didn't give them a reason to pull my credit without my consent. He said if I wanted the inquiry from my credit report, that I would have to contact XXXX  because they wouldn't do it. I again told him I never heave then authorization to pull my credit ( sounding like a broken record by then ) and that's when he stated that once I started the application, that my credit was automatically pulled. " So, the credit check is implied? That's what you're saying? '' I asked, which irritated XXXX to the point where he stated that I was " asking him questions he had no answers to '' or something to that effect. He then asked if I would like to speak to his supervisor, which I replied I most definitely would. Once I was transferred to her, more of the same thing. The major difference being that she did email someone about how the credit check went but could still get no definite answer. 
Today I called XXXX  to try and get them to take off the inquiry, and was told that since I knew who the company was, it was not considered fraud and that they could not take off the inquiry, that I had to make contact with Carvana and get them to lift it, which they won't! How could they check my credit without me even knowing or agreeing to it, or completing and signing any documents and contracts then submitting them?