You basically asked,
Do banks "hold a grudge"?
Many banks do indeed "hold a grudge" in the sense of using data about prior relationships with you to make decisions about potential new business.
Banks retain customer information about closed business. This is required by regulators to a certain extent, but it also helps banks track customers who have caused them losses. Many banks will indeed "blacklist" customers who have caused losses, and many lending platforms have functionality that automatically flags members who have caused losses in the past. Sometimes this process includes a threshold (i.e. the loss has to be more than $500) or it acts as a soft factor (the loss simply means that the credit application will be flagged for manual review, and the info on the loss is presented to the human making the decision).
There is also some variability around time frames - some banks will only flag a customer for a certain number of years, whereas others will keep the flag "permanently" (in quotes because it may be intended to be permanent, but as technology changes and data is converted/archived over times, who knows if it will literally be forever).
In a comment, you got to the root of your question when you asked,
That's pretty much what I was looking for... whether ALL banks follow the same "formula" (solely based on your credit report) for approval/denial or if they can factor in their own criteria, that would surely include history from past customers.
The answer to that is certainly that banks do not all follow the same formula. Further, the formula will vary significantly even within a specific institution, depending on the customer and the product they're seeking. Small, less-risky lending products are almost always approved or denied by software, based on a pretty short list of factors (self-reported income, credit score, etc).
Larger and riskier products are more likely to be approved by humans, and almost always include some degree of subjectivity. For instance, if you're applying for a car loan, the lender will likely look at the details on your credit report for any car loan that's listed, to see how you behave with respect to car loans. So - even if you have an okay credit score, and plenty of income, you may still have problems getting the loan if you were consistently late on paying your last car loan. It might not even matter if that other car loan was with a different lender or not.
Unfortunately, the variability in practices makes it hard to provide an answer for a specific product and situation, and essentially, banks can (and will) use just about any data they have in order to make decisions, as long as the data isn't illegal to use for decision making (i.e. discriminatory things like what race you identify as).
