We class Red Mullet a Mediterranean Fish, falling between oily and non-oily species. We are very fortunate to have good sized red mullet landed around the Cornish coast. As it happens it is quite unrelated to Silver Mullet.
Red Mullet grows quickly and matures young, so if caught in UK waters, as all of ours is, it is a good sustainable choice. They are usually landed by day-boat inshore gill netters.
They do need to be super fresh as they get soft very quickly - that is why you do not tend to see them in supermarkets as the supply chain is too long!
The Romans took freshness to a whole new level though, apparently having them brought to the table in bowls of salt water still alive! Ours are almost, but not quite, as fresh as that!