No one should find the title statement surprising.
It requires little thought to understand why consumers of school lunches should expect a lower quality meat than that expected by consumers of meat based fast foods in the private sector.
It all goes to the competition for scarce resources and revenue available to bid for these resources. An individual (any legal entity) cannot consume more than they produce, including the present consumption of future production through the use of credit, without the fear of bankruptcy.
In order to consume, the government must obtain the product of its citizens, either through taxation, borrowing, or through the process of inflation, devaluation of the medium of exchange. This places an absolute limit on the funds available to bid for the quantities and quality of meat needed to supply the nation's school lunch program. The school lunch program's product, meat foods, is not totally paid for by the consumers (school children, faculty & staff) of the product, but is partially subsidized by the taxpayers of the nation.
Businesses do not face this problem, since all business activity is financed by the demand for their products offered by their customers. A business can afford to bid on a higher quality of meat, since the expense will be covered by the sales of the final product to their customers, or the business will no longer exist. The funds available to purchase the factors of production of a final product are directly related to the demand for the final product. The fast food restaurant's quality production, meat foods, finances its consumption of quality meat, whereas a governmental agency has limited funds available to compete and pay for higher quality meat, and to finance the internal quality control systems during the process of preparing the final product.
No amount of new regulation, new policies, or increased taxation will remedy this situation, since any government agency's budget will have a finite limit, that is not expanded by the demand for that agency's activity.