What your argument ignores is the key component of the link in question: the animals were too sick to be consumed. While you are correct in that factory farming

What your argument ignores is the key component of the link in question: the animals were too sick to be consumed. While you are correct in that factory farming allows lower income people access to meat, you overlook the fact that the meat they have access to is poor quality, unhealthy and often contaminated. You wouldn't answer the claim that X group of people doesn't have access to clean water by saying 'well at least they have access to water.'