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In order to legally check someone's credit, you have to give explicit written permission (before I went back to grad school, I worked as a Purchasing Agent and would occasionally run credit checks on prospective subcontractors who did business as individuals). In most states, it needs to be a dedicated, one page form that is written in clear English. That is, it's unlikely that it's something that they sneak into some general terms form that you click "I agree to" online without really reading. Also, you can get into a lot of trouble by running a credit check on someone without their expressed written permission, so I doubt that schools would risk that (plus it costs $10-15).
Now if you're applying for an immigration visa, it may be different and I have no knowledge of those procedures other than a general sense that financial self-sufficiency/wherewithal is one of the criteria for granting a student visa. But in terms of the admissions process, I don't think that it's something that you have to worry about.
On the other hand, when you go out onto the job market, prospective employers may look at your credit report.