That's how I would interpret his/her remarks. The federal government was intended to favor no person or group or discriminate between no persons or groups but apply the same rules to everybody regardless of age, race, gender, religion, political affiliation, or socioeconomic status. The federal government imposed no such requirement to the states, local communities, or individual persons or groups, however.
So as it was intended, the federal government could not dispense charity or any other government provisions to some but not all as that would violate the equal protection under the law concept. But the states and local communities could. The federal government could not deem one person unworthy for service or accommodation, but the individual citizen could. The Founders deemed that liberty could not exist if each person was not master of his own person and property.
Of course over the last hundred years or so years, power greedy politicians and the courts they put into place have corrupted that principle again and again as more liberties have gradually been taken from the people and more power transferred to government. And I believe the nation is far worse off because of it.