First of all, thanks for asking this question. You prompted me to go ahead and buy Nimura’s Daughters of the Samurai, which has been on my reading list for a while.

On the whole, it's a pretty accurate entry, though there are some errors and you’ve caught a big one. From what I've seen of his work, the creator Jason Porath does a good job of a) trying to read widely and source everything b) and more importantly, welcoming corrections, quibbles etc. He has a feature on his site where he gives out certificates to anyone who corrects him/adds an insight. An example: http://www.rejectedprincesses.com/blog/corrections/catching-up-on-corrections

This approach puts Rejected Princesses heads above most popular history sites. It won't always be accurate, but the creator always wants to learn.

The big error here is that he’s misattributed a quote from another one of the Japanese women students to Sutematsu. The quote: “My country will never become advanced until her women and mothers are educated” is actually attributed to Shige Nagai in Nimura’s book. Shige studied at Vassar as well, but at the School of Music.

Nimura didn’t actually claim Shige was a valedictorian, either, though she used the word “valedictory,” which was probably part of this mix-up. Shige said this to a newspaper just before she left San Francisco for Japan. Here’s the quote in full from Nimura. (p. 823, Daughters of the Samurai)

By OCTOBER, SHIGE was in San Francisco, ready to embark on the steamer Oceanic, bound for Japan. The city that had gawked at her nearly a decade earlier was now admiring, if still faintly patronizing. "Through her connection with the Abbott family she came into close association with other famous literary families of New-England, and imbibed the spirit as well as the habits and customs of those with whom she lived," reported the San Francisco Chronicle. "She is now a graceful girl, with petite figure, bright and intelligent face, and polished but unaffected manners, dressing prettily in American costume." A "thorough New-England girl in all her instincts," she offered a ringing valedictory comment:

My country will never become advanced until her women and mothers are educated, and our women will never, as a class, be educated so long as they marry so early, for the years from 15 to 20 they should spend in school.

Nimura is using “valedictory” here to mean a farewell to the United States, not a university speech. (I checked newspaper archives to make sure Nimura had the context correct here, and yes they were comments to the Chronicle.)

However, does that clear up the subject of Sutematsu and the valedictorian status? Weirdly enough, it doesn’t! She’s noted as a valedictorian at Vassar in many other works, as you’ll find if you search Google Books. No doubt those descriptions of her filtered through in Porath's entry on Rejected Princesses. Nimura’s book, however, is the best researched, and I think it explains the matter (pp. 87-88):

The weather held for commencement the next morning. At 10:30 the graduates took their seats in the front rows of the chapel, surrounded by alumnae and guests; the Japanese consul in New York, Saburo Takaki, was present with half a dozen of his staff. His government had provided Sutematsu with lavishly embroidered silk for her graduation dress, and the audience murmured as she stood before them, one of ten senior speakers.

So, under the definition of a valedictorian as a student who gives an oration at graduation, Sutematsu was a valedictorian, but she was one of ten. She wasn't the top student in her class, though, as you noted. What Vassar at that time actually defined as a valedictorian, I haven’t determined.

Sutematsu’s speech wasn’t about women’s education, but foreign policy.

Consul Takaki was not disappointed. Where her fellow orators had chosen as their themes "The Conscience of Science," "The Decline of Speculative Philosophy," or the relative merits of Alexander II, Sutematsu addressed "British Policy toward Japan," condemning the unequal trade agreement that persisted between the two nations. The speech was "the most interesting of the whole series," declared the Poughkeepsie Eagle, "an eloquent plea for the independent nationality of Japan." The Chicago Tribune called it "the most notable, as it was the most enthusiastically applauded oration of the day." Sutematsu had proved herself as canny as she was eloquent: without directly criticizing her adopted country, whose policies toward Japan were similarly patronizing, she had made her point nonetheless. The original goal of the Iwakura Mission—treaty revision— remained incomplete.

News of Sutematsu's achievement reached all the way to Japan. 'Never before had a foreigner's speech moved an American audience so much." trumpeted the Asahi Shinbun. "Miss Yamakawa brought great honor not only to herself, but to her country." Tomomi Iwakura and his ambassadors, many now among the most prominent figures in Japan. never imagined they would read such news of the little girl who had traveled with them.

This speech actually strikes me as a lot more interesting than the one Porath misattributed to her. Shige’s comment about education readying women for motherhood was progressive for the Japanese context, but fairly tame for a Western audience. Sutematsu was a Japanese woman directly taking on Western colonialism in her speech, and she got praise for it!

One interesting fact Porath doesn’t mention in his entry is that all five of the girls sent with the Iwakura Mission to study in the United States came from families who’d been on the losing side of the Boshin War. The reason is that the Meiji government could not get anyone in a position of power to send their daughter abroad. It was the samurai families who were facing difficult prospects now for their children who were ready to send their girls off to America. However, the Yamakawa family put a huge value on education, and a genuine belief in the importance of Western education motivated her older brother in sending three of his younger siblings abroad.

More quibbles: Her American host family didn’t really change her name to Stemats. (Or 'Stematz' as Vassar wrote it.) That’s basically how it’s pronounced, or as close as they could approximate it in English. The “u”s in Sutematsu are mute vowels. Nowadays, there’s a standard way of transliterating Japanese, so we write Sutematsu, back then they went with how it sounded. Su-te-ma-tsu would have been the incorrect pronunciation here.

As for "the most educated Japanese woman alive", you're right that this is hyperbole. Sutematsu was the most Western-liberal-arts-college-educated Japanese woman, but as the Rejected Princesses entry says, she lost the ability to speak Japanese fluently and had to regain it. She certainly wasn't being educated in the literature and culture of her homeland.

It's mentioned in this entry that she became friends and allies with the Japanese empress. Empress Shōken herself was a brilliant prodigy from a noble family who was picked as the imperial consort precisely because as a teenager she was remarkably well educated in Japanese and Chinese literature, art, drama, calligraphy, music etc. The empress also threw herself into Western studies, as far as they were available, and became a huge figure in Japan's social reform. Someone could claim she was the most educated woman in Japan. (For more information about Shōken, check Donald Keene's Emperor of Japan:Meiji and His World.)

Or what about medical knowledge? The first registered woman doctor in Japan was Ogino Ginko (1851-1913). She studied medicine at an all-male Western medical school in Japan, fought for her official license, and founded a hospital where she specialized in obstetrics and gynecology. Someone could argue that this sort of scientific Western education trumps a Western liberal arts education or a Japanese elite cultural education. (For information about her, consult Ellen Nakamura’s article: Ogino Ginko's Vision: "The Past and Future of Women Doctors in Japan, 1893 https://www.jstor.org/stable/42771973 )

As I believe you were hinting, there’s no real point in trying to say who was the best educated. All these women were part of a wave of well-educated, smart, passionate Japanese women who helped transform their society.

BTW, footnote 9 in that post suggests that the valedictorian information came from the cited book:

That’s a direct quote from her valedictorian speech, in which she laid out a forceful argument about the unequal trade relationship between the UK and Japan. She was a smart cookie.