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As long as it was a SOFT inquiry, lenders won't see it.
In the case of Cap1 when you request a CLI they softpull your credit. This means you and they see the credit pull, but no one else can see it. It doesn't change your credit score, it doesn't factor in any way in a financial model or predictive pricing, bankruptcy, spending, or underwriting system. Cap1 Auto Finance can see a Cap1 Credit Card denial and the other way around - as well as the reasons, but that's as far as it goes.
The reasons do not go back to the bureau to be shared with others. It doesn't even work that way when it's a hard pull. The credit bureaus have nothing to do with the decisions and do not receive that information. So other creditors have no idea of those decisions.
I know it's hard to believe the bureaus especially given Equifax's irresponsible handling of its data breach, but I assure you that's how it works.