So far, at least 44 cases of lesions—about a third of them known to be malignant—have been identified in 21 species of chondrichthyan (the class of jawed and finned vertebrates that include sharks, rays, and skates), as marine biologist Charlie Huveneers and colleagues report in a paper published last year.

But such tumors are rare, it seems—or at least hard to find.

Even after Huveneers, who runs the Southern Shark Ecology Group lab at Australia’s Flinders University, and a team of Australian and American scientists managed to biopsy one funky-looking mass in a shark’s lower jaw—the researchers snagged the tissue from a free-swimming, 14-foot great white using a souped-up harpoon (the ultimate outpatient procedure)—it was hard to determine whether that tissue was cancerous or not. (The team’s best guess is that it was benign.)

And thus, the belief persists: Sharks, if not quite immune to cancer, appear somehow resistant to it.

The support for this theory isn’t just the absence of evidence (the lack of shark sightings at the cancer clinic). It’s also biological. Shark cartilage is avascular: It doesn’t have blood vessels winding through it. What’s more, over the past few decades, research teams have isolated proteins that appear to inhibit the creation of blood vessels, a process known as angiogenesis. Given that cancerous tumors need blood to grow and spread (and, indeed, a hallmark of cancer is the ability to recruit blood vessels through protein signaling), the fact that shark cartilage is apparently anti-angiogenic is tantalizing.

Now, to ratchet this tantalization (<< real word) to Shark Week-degree, there’s more: Several research studies have found that isolated shark proteins do appear to inhibit cancer cell growth in Petri dishes.

But NOT in human cancer patients, sadly. It doesn’t work, folks. In one controlled study after another, shark cartilage extracts have not reversed or halted the disease. Nor have these compounds worked in animal models. (The National Cancer Institute has a great, up-to-date, and comprehensive summary of the efforts here.) Ingesting the stuff, moreover, might even harm you—to say nothing of the sharks themselves.

And that brings up a great challenge for medical science, particularly since the dawn of the Internet and the muddy dusk of social media. While there’s nothing wrong with pursuing such natural-world clues through experimental science—this process, after all, has yielded medicines from penicillin to the cancer drug Taxol—there is the ever-present danger that desperate patients will cling to the clues without following the evidence to its conclusion (and that wily marketers will help them do it).

If Shark Week teaches us anything, it is that hype begets hype. That’s great for TV ratings, surely; not so great for medicine.

One can’t tell, perhaps, from a cladogram, but in the kingdom of medical manias, shark cartilage and snake oil are first cousins.

This essay appears in today’s edition of the Fortune Brainstorm Health Daily. Get it delivered straight to your inbox.