Is there some sort of rule/law/statute that I'm not aware of that makes it a requirement to open at least a savings account (usually referred to as a 'thrift savings') for anyone, regardless of whether or not they qualify by your's bank's policy?

Based upon my research, it would appear that the Minnesota Congress has declared through the Minnesota State Statute 47.76 that a “required savings account” or commonly known as a “thrift” account, is an available account wherein A federal or state chartered financial institution, including, but not limited to, a bank, savings association, savings bank, or credit union, shall offer to a Minnesota resident a savings account to promote thrift that has no service charge or fee, if such an account has an average monthly balance of more than $50.
Analysis given by the Minnesota Bankers Association explains that Minnesota law and oversight is generally silent regarding accounts that have been deemed a “thrift” account. Banks are legally allowed to impose minimum balance prerequisites for the earning of interest or may condition the payment of interest on adherence to the prescribed number of withdrawals occurring during a period. The Minn. Bankers Association ends their analysis by reminding that their is no obligation on the part of federally or state chartered financial institutions to promote these types of accounts, however banking institutions ought not to try to conceal the existence of these accounts.
Further articles under Minnesota State Statute 47.77-47.79 relate to the ability of financial institutions to close, transfer or in anyway alter the preexisting agreement between account holder and the originating institution.