The financial institutions I can understand them checking for illegal stuff and doing their background checks. Like you say, they cannot hold anything against you if your credit history is shoddy. Its non of their business.
It will be very hard to prove that is why you did not get the position. They might just choose the guy who does not have financial issues. If someone is in trouble financially they might be more likely to submit fraudulent time sheets for instance, might be off sick more with higher stress levels, all sorts of things.