“NY gives driver's licenses to anyone.”? No, knownothing; as a matter of fact, NY does not. NY gives DLs to those eligible for a DL under NY law. NY won’t give me a NY DL unless I go jumping through some hoops that I don’t want to do for at least now.
DHS approves GE for lots of people even without DL data. DHS doesn’t need NY DMV data; DHS just wants to make a fuss about NY DMV data for reasons that are motivated by something other than doing background checks on GE applicants.