Of course not. Many companies won't want the bad publicity and would simply remain silent in the face of such an occurrence. Public health officials should be allowed to do their jobs and warn the public about possible dangers. Big business has proven time and time again that they put money over human health and safety.
Discretion should not be left to companies. That is what often leads to business problems in the first place. If we have government supervision over companies productions of food, then it will be safer in the long-run. There are hundreds of millions of Americans that rely on private food companies, and they need protection.
I think there needs to be some unbiased regulating agency that has the authority to deem what needs to be recalled, especially when its in the field of health and has the potential to result in an outbreak. I think if it is up to the company what to do they will be swayed to do the best thing for the company and keep things quite and hope for the best.
Product companies should be given a very brief amount of time to voluntarily recall their products, and this should be regulated by law. Refusal to do so should result in immediate forcible recall, along with fines and even footing the bill for the state's trouble. Accidents happen, mistakes can be made, but a company with self-interest in its public image and corporate pockets to line with money can very rarely be trusted to do the right thing, especially when no one is looking.