First, people who are already rich don't get RICHER by using their credit card. They are spending money so technically they have less money after all the purchases. Yes, as with ALMOST ALL credit cards, there are PERKS beyond delaying your payment. But people don't get rich off credit cards.
Second, a credit score does not define or indicate how rich you are. My 77 year retired old mom who lives on $21,000 a year income (Social Security and her small nest egg) has a credit score of 749 which is considered "very good". She was actually over 800 for the past few years but when she went into the hospital last Fall and failed to pay ALL her bills for 2 months, she got rightfully dinged on her credit score and it was lowered to 650 ("fair"). It has been slowly climbing up every 3 months. Credit scores are determined by 1)how much total revolving debt you have, 2)how much possible credit card debt you can rack up (such as having a $15,000 credit limit on 1 card and a $10,000 credit limit on a 2nd card), 3)your payment history (late vs. on time), 4)length of having credit, and other NON-INCOME factors.
In a very broad statement, you could propose that poor people (define poor please) may have lower credit scores and that proposal could be somewhat accurate. But the REASON is not because they are poor...it's because of other factors. Heck, there is a fair percentage of the USA society that does NOT have credit simply because they pay with cash and do not own any kind of bank account. Trust me, the banks, credit card agencies, and government would love to get them somewhat off cash. The banks and credit card agencies would earn money while the government would be able to track their money flow and tax them appropriately.