an anarchist would not interpret regulatory bodies as "big government", because it would reject the underlying premise of property rights. the government does not exist to regulate the market, but to protect it from regulation. regulation - real regulation by democratic or scientific bodies, not captured industry bodies - is consequently a way to break through the statist system of property rights and assert control by the people over their own resources.

regarding meat....well, maybe we shouldn't really have slaughterhouses. but, if we're to have slaughterhouses, they should belong to the people, and not to corporations. what currently prevents the democratization of resources is the government, through it's enforcement of property rights. regulation is consequently not about the government "interfering" in the realm of "private production", but about the people abolishing the state's control over resources, through the tyranny of property.

what removing the government from the business of meat processing means is abolishing the property rights used by private corporations and setting up local councils that distribute the meat on a needs basis.

nonsense about "free markets" is exactly that.