This author is wrong. You may not add onions, avocado, or any of those other things to a grilled cheese sandwich, at least not if you are trying to make a grilled cheese sandwich. Once you start adding veggies or meat, it becomes a melt. There's nothing wrong with a melt! But words mean things, and you can't just call any sandwich you like a grilled cheese just because the bread is toasted and it has melted cheese inside.
I disagree, or rather I don't care if I'm wrong but there are likely millions on my side. I'm 49 years old, grew up eating grilled cheese (American cheese on Pepperidge Farms white bread), often with sliced onion or tomato, and mustard. I had never even heard of a melt until I was probably 35, and even so, I still call a doctored up grilled cheese sandwich a grilled cheese sandwich. It ceases to be grilled cheese only if meat is added.