There is no law that says lenders can only pull X for Y product. So basically lenders can pull any report they want as long as they have a "permissible purpose". Any logical reason could be classified as permissible purpose. Let me give you an example that applies to your case.
Ally is bank and a car loan is banking product. Ally wants to know your relationship with your current or past banks. If you have a history of NSF (bouncing checks, overdrafts etc) that could be an indication of wether you will make on time payments of a future loan.
This recently came up with the Apple Card. Durring the first wave there was a lot of rejections from people who were confused because they thought their credit was perfect. Well GS was pulling reports from some obscure credit agencies and also pull ChexSystems.
My DW recently obtained an auto loan through the dealership. One of the lenders it was sent to was Ally Financial, although she didn't end up getting the loan through them. Upon getting a copy of her Transunion for something unrelated she saw in the summary that Ally pulled her Chex Systems and DDA history. When seeing this she requested her Chex Systems report and yes they pulled it for an auto loan application. She has nothing negative on her Chex Systems but just curious how her Chex Systems is relevant to an auto loan and can lenders do this? She was applying for a auto loan not a checking account so why pull her Chex? Any feedback would be appreciated.
Unfortunately, there is a trend now for many lenders and places you wouldn't expect to pull as many reports about you asa they can get their hands on. I rented an apartment in 2014 and they approved me, but they pulled my Telecheck report and it showed that I had bounced a check, so they allowed me to rent the apartment, but I always had to pay using certified funds. I also applied for the Apple credit card a while back. While I was denied, I did see that they pulled Innovis and Chexsystems, in addition to my TU report.