The last sentence is sort of a tautology because supernatural is not well defined. Any set of features can be called supernatural.
Every species of animal is bound to have some unknown morphology because evolution maximizes diversity. In order to be called a species, it has to have a set of features that are not shared by other creatures.
There have been creatures described by local people that were unknown to the broader world and discovered. None of these creatures have violated known physical and chemical laws. However, they can be fairly weird, anyway.
My favorite television series is 'River Monsters'. This is a wildlife series (reality series) where the host (?), Jeremy Wade, looks for dangerous fish all over the world. He has discovered one or two new species of animal, as well as unusual varieties (subspecies) of known species of animals. He finds rare animals, and even unusual behavior patterns in known species of wild animals.
None of the fish satisfy the my perception of supernatural. None of the animals that he has found violate any law of physics or chemistry. Very often these fish are well known to a small group of people in the region. So in a very loose sense these animals are legendary. Often, the locals have a partial information on this. Sometimes, he talks to shamen and priests who have some religious beliefs and superstitions associated with the animal (almost always a fish).
He photographs these creatures when he catches them. I know the show is edited and the scenes selected. However, he goes through the general process of finding these creatures. He talks to locals, he goes to the fishmarket, he photographs the lake and in the end photographs the fish! He measures it, weighs it. He shows the thing to qualified biologists.
So in a very general way, he investigates cryptozoology. The creatures have some rather unusual characteristics around them. There are magical beliefs associated with them.
This may be naiveté on my part. However, I think his work is real science, whatever that means. He photographs it. He ways it. He wrestles with it. He documents the entire process. He shows the animals on public television, open to loads of scientists. I haven't heard any scientist call Jeremy Wade a fraud.
He has 'discovered' a gigantic variety of electric eel unknown to science that was caught by an Indian tribe. He discovered severely deformed catfish in Chernobyl where the nuclear reactor melted down. He discovered an unknown species of stingray in the Amazon.
However, I do not consider him a crank. He catches the fish on tape. He shows the photograph. He investigates the ecosystem before he catches the fish. He talks to biologists. He shows the interviews with the locals.
Wade doesn't call himself a cryptobiologist. The typical 'cryptobiologist' doesn't do this level of homework. I don't know any self proclaimed cryptobiologist who actually catches the fish and shows us photographs. There is no taxonomy. There never is a body. The photographs are blurry. It is all trace evidence.
