For what it's worth, I'll toss in a little biology behind the words of caution.
With most elasmobranch species, they store excess fat in the liver first, then around the heart. The liver storage actually restricts the blood flow to the organ, and limits the ability of it to function. Slowly, it starts to have a negative impact on the kidneys as well, leading to poor blood filtering. You end up killing them by blood poisoning. If that doesn't happen, you are also starting to restrict the movement of the heart, making it work harder to pump blood to the rest of the body.