I've eaten a lot of cans of food in my day, and I can say with certainty that they are not all the same. That's not to say that the expensive brands are the best though.
Maybe it's different in the USA, but there's definitely a huge variation in quality across canned goods in Australia. Most cans under a dollar aren't worth buying in my experience.
They aren't all made in the same factory either, the cheaper cans tend to be made in Indonesia or other developing countries. I try and avoid food manufactured in developing countries, I've seen what their food safety standards are like, not to mention the pollution and heavy metal risk, or if it's even what it says on the can (even Europe isn't immune to this, see the Horse Meat Scandal). I have no particular reason to believe that my can of Tuna from Vietnam actually contains Tuna, or that it's free of mercury or lead.
A 50 cent can of baked beans or spaghetti doesn't taste anything like a proper Heinz can, the beans are usually fine but the sauce is atrocious. But there are brands that are cheaper than Heinz that are just as good (don't taste the same though).
Cheap cans of fruit are almost universally terrible. The fruit in the tins is terrible quality: underripe, overripe; too sweet, sour, or bitter. Bottom shelf tinned pineapple feels like I'm eating timber.
Vegetables tend to be fairly consistent, although the cheapest cans of tomatoes often contain added water or tomato juice.
Coconut milk/cream is worth paying for the premium brands, the budget brands are so watery. Pacific Island sourced coconut milk tends to be better, at least in my opinion.
Fish is a real mixed bag. Not just for taste, but for sustainability, human rights, and pollution. It's worth doing some research into what brands are best. Some of the more expensive brands are actually the worst.
Plain legumes (chickpeas, lentils, kidney beans etc.) are the only canned goods where the cheap brands seem to be the same quality as the premium brands.
Your statement [branding often has little relationship to quality] still stands though. You can get high quality, cheap packaged food, you just need to spend a bit of time looking for the right brands (which may involve trial and error). Going for the most well known or most expensive brand is definitely not the way to ensure you're getting the best quality food at a modest price.