If ‘the sea’ includes coastal marshes that are only underwater at high tide, that significantly expands the nutritional palette - a lot of coastal plants are superb sources of vitamins
…ironically.
Well, spoilers for a 150 year old book follow:
Captain Nemo is probably lying anyways, isn’t he? Or at the very least “the sea” includes everything growing on The Mysterious Island
The book (not the movie) mentions them milking whales (!) I forget how they convinced the whales to hold still.
I found an article called Vitamin C in East-Greenland traditional nutrition which is a modern reanalysis of data from the 1930s. They found intake of vitamin C was around 20 mg/day from seals, another 20 mg/day from algae, and 6 mg/day (female) or 14 mg/day (male) from fish. They also got lesser but significant amounts from terrestrial plants. Humans need only about 10 mg/day to stave off scurvy, so vitamin C deficiency should not be a big problem. Seal organs are a richer source than muscle meat, with adrenal glands being especially rich. They also found, contrary to earlier findings, that muktuk/mattak (skin and blubber of marine mammals) is not a particularly good or important source of vitamin C.
Seinfeld:
Jerry : What the hell is “Chicken of the Sea” Tuna? There’s no chickens in the sea! What, are they afraid to tell us it’s a fish? Think we won’t understand? “Just put chicken on the can. They’ll think it’s chicken that lives in the sea.” I don’t want any chickens that live in the sea! Chickens on land, fish in the sea! Don’t put chickens in the sea!
They could maybe market chicken as “tuna of the land”? 
Tuna of the Dirt has been called the analog a number of times.
Humans can’t make Vitamin C, which is gonna be the problem here. Not much in in seaweed. Some in raw fish. If you can gather Phytoplankton there is some Vit C.
Other than that- you are good. Now on “Cast Away” he did have some land based plants.
Kind of undercuts his argument about how edgy comedy was before political correctness.
Seinfeld is a decent comic who created a great TV show. Although this show had some controversial moments, Jerry’s stand up comedy was never particularly edgy. So much so that it was used as a barometer by other comedians; “if you are offended by the comedy of Jerry Seinfeld, then F- Y-” (implying you would be offended by anything).
Why do folks think there isn’t much vitamin C in seaweed? Most plants make vitamin C, and my default assumption would have been that seaweed is an adequate source of vitamin C.
Beneficial Vitamins in Seaweed | Wild Irish Seaweeds.
Says “Carrageen , Sugar Kelp, Bladderwrack and Nori have great amounts of Vitamin C”
Okay, maybe that’s not a super source.
This looks solid
It concludes that raw seaweed is a mediocre source of vitamin C.
Seaweeds are not a rich source of vitamin C, but when consumed they feed into the daily intake. To reach the Recommended Nutrient Intake approximately 400 g ww of seaweed should be consumed per day, which in contrast to rosehip is 5.35 g ww.
But rather annoyingly, the article says that amounts of vitamin C vary a lot by species, but then mostly focuses on averages over whole genera. Even so, eating 400 grams of raw seaweed seems doable. And if you figured out which sea weeds are richer in vitamin C, you could do better.
Which is what I meant when I said “not much”. But if course the amount varies. Let us take kelp- very common, large amounts and the bladders can be made into pickles- or even eaten raw. It has 3mg per 100 grams. A dude needs about 70 mg /day So you’d need to eat 23 X 100 grams or over two kg. That’s a lot.
But yeah, if you could find some of the rarer seaweeds, such as bladderwrack, you’d be okay. Like you said-
Of course Verne didnt know about Vit C, that was 50 years after the book came out.
As mentioned above, raw fish has vitmain-C in it. So, combined with seaweed it seems very doable if you have access to those things.
It seems you could live on things that only come from the sea but, ideally. you’d have some land based food too (fruits, coconuts) ala Castaway.
I just wonder where fiber in the diet is coming from? I’d think it’d have to be seaweed or nothing on a sea-based only diet. I am not sure what happens if we do not get fiber. I am not sure I want to know.
Kelp has 1.3 grams per 100 grams…
https://fdc.nal.usda.gov/fdc-app.html#/food-details/168457/nutrients
No one is arguing that this is an optimal diet. Just one which is possible.
Relevant Straight Dope Article - if humans evolved from the sea, we may have been able to handle a 100% marine diet!:
They found the corpse of a nursing female baleen whale that had, supposedly, been killed by a cachalot or sperm whale, and extracted the milk from its body.
Just don’t try eating walrus and polar bear livers. They contain toxic levels of Vitamin A, so all your skin falls off and you die.
Symptoms of polar bear liver poisoning depend on the amount of liver consumed but usually include weakness, vomiting, diarrhea, drowsiness, headaches, hair loss, bone pain, peeling skin, and blurred vision. At very high vitamin A levels, symptoms include full-body skin loss, hemorrhaging, coma, and death.
Now what am I going to do with these walrus livers I got at Costco? It was too good a deal to pass up.