"Leveling" here means making people more equal - but not in some socialist sense. Rather, socio-economic differences are reduced when bureaucracy pushes decisions, distinctions, etc. to be based on rational criteria rather than ascribed statuses. The flip side, to a critic, might be that this then legitimizes those differences that remain (since they must be based on rational criteria).
Much of our rhetoric of "fairness" relates to the general idea of "due process" - we require of decisions that they are made according to rules and criteria that apply the same to everyone. It's not one rule for that group and another rule for this group. In this sense, the rule or rules levels out social differences that might otherwise hold sway.