Okay. So it kind of makes sense because viruses often enter the body via mucosal membranes 粘膜, which is found in the respiratory tract and the gastrointenstinal tract, so your nose and your mouth, and the subsequent connecting tubes. (These are thin epithelium, so easier to penetrate than the layers of the outer skin.) While the idiom implies that viruses enter with your food, it really just enters through your mouth, regardless of if it's carried by food or otherwise. The saying has some truth to it, but it is not an excuse to use imported fish as the reason for an outbreak. That is, to simply put, a cover-up. The current data is suggesting that surface spread is not the primary route of COVID-19 transmission.
HAV is spread via what is called the fecal-oral route. Somebody infected went to the bathroom and didn't wash their hands afterwards. And touched things smearing invisible viral particles onto food and containers. Somebody ate that food and got infected. Thus it is common to see Hepatitis A outbreaks in connection with restaurants with the source being a restaurant worker. So, yes, this is a hygiene issue.
As for H5N1 and H7N9, these are influenza viruses which primarily transmit via droplets. SARS does the same. Droplets, so sneezes, coughs, and spit. In short, it comes from one person's mouth/nose to another's. How surfaces (or fomites) help transmit is the droplets can sit on these surfaces until somebody comes around and touches the surfaces and then rub their eyes or nose, or wipe their face. This then transfers the viral particles to the vulnerable mucosal membranes. This is why there is widespread use of masks; what it does is NOT protect yourself. Even when wearing a mask, you can use your hands to adjust the mask or still rub your eyes. You can still get infected wearing a mask. But wearing a mask will block your respiratory droplets from getting into the air. Influenza and SARS both are primarily droplet-based spread. It is to heavy to go airborne and stay afloat in the air. There is data suggesting that COVID-19 is light enough to be aerosolized, or carried in the air by smaller water droplets. (Even though COVID-19 is a cousin of SARS.) Either way, spread of these is more about being in close quarters with sick people. Being crowded in a restaurant. Having a party in someone's house. A large exhibition in an enclosed convention center. COVID-19 is extra annoying because a large percent of infected do not exhibit ANY symptoms, and thus can be spreading the virus without even being aware that they are sick.
None of these are foodborne diseases. Foodborne diseases are typically bacteria, fungi, and parasites. Yes, to get infected the viruses have to enter either your nose or mouth, but the viral particles are generally not carried by food.