I'd be pretty surprised if I bought a product named "Just Mayo" that didn't contain actual mayonnaise, but I guess it fits into the same pattern as American "cheese".
Margarine with yellow dye trying to look like butter (also dyed yellow).
"Milk" products such as almond milk and soy milk when both are just juice since neither almonds or soybeans have nipples.
There must be some law to prevent such desception.
I think the American "cheese" thing is a bit of red herring too. What people are actually referring to is the fact that it's actually a cheap, heavily processed product that doesn't really bare any resemblance to cheese as we have known it before. This complaint about American cheeses is not usually dished out to, say, Treeline's nut cheese brand — presumably because it looks like "real cheese".
It seems incredibly arbitrary to just pick one ingredient and say "hey, this is what makes this a real version of [x]", especially when that ingredient is apparently so unimportant to the actual consistency and flavour of the product. It's as if we'd arbitrarily decided that something would stop being mayo if the type of oil wasn't canola or something.
No one has "arbitrarily" picked a single ingredient to define real mayonnaise, you'd have the same reaction if someone tried to replace the vegetable oil with lard, or the vinegar with sulphuric acid. The basic recipe for mayonnaise is pretty uncontroversial.
As for having the same taste, I'll believe that when I taste it. That's what Coca-Cola says about Zero as well. It's just marketing, they're not going to say that the product they're passing off as real mayo doesn't taste like mayo.