I don't know that you can do anything about the event that happened in the past itself, but you can find out now if you/she can get a bank account and if not, why you were denied. To be clear, there are federal consumer protection laws that require "adverse action" to be presented to you in writing, with the details of the consumer agency/report that contained the information they used to deny you, and they generally also must include at least a generic reason.
You are not alone in having this sort of issue, though, as testified by the Times article Why Banks Might Refuse To Take Your Money. Noted in the article was security "flags", like not getting issued a security number until age 30 due to immigration - and this was cited as enough to deny a bank account. You are also entitled to free reports annually, regardless of whether or not you were denied an account, and these are called "speciality consumer reports" (link to government website detailing them and your right to receive a copy.
So banks are generally allowed to turn you down for effectively anything, but they aren't allowed to keep the "why" a complete secret. They don't have to tell you on the spot, but they do have to provide written notice.
As to the "why", it may have been related to how long her social security number has been issued, potential identity theft or error in the report (someone was using her social security without either of you ever knowing, or a company/bank reported the social# with a typo), lack of previous history (never had a bank account that showed up on any reports), etc.
Getting A Bank Account Anyway
I strongly prefer to deal with smaller (local or regional) Credit Unions - I really dislike the consumer practices of most of the larger banking system, and find the services and treatment to be far superior at credit unions. So I'd try to apply there first. If that doesn't work, then get that rejection letter and request your report right away!
If it is an issue with lack of credit/account history, you might consider requesting alternatives - such as being a co-signer/joint-holder of the account with her for 6-12 months, or opening a savings-only account (they even have those for kids!), or look into opening an Online-Only account from various legitimate online banks.
It might take a few tries and some ever-so-fun bureaucratic paperwork, but you should be able to get a bank account you can use, or at least a reason as to what's making it so hard. Money laundering and anti-terrorism legislation might very well have made this process more restrictive or outright ridiculous in some cases, but you can usually still work the system with some time and effort.
There may very well also be less moral reasons involved, such as discrimination which may or may not be legal. But it's impossible to know any of that based upon such a limited-information scenario, so I encourage you to at least get a useful credit report or a proper rejection letter so you have more info to go on.