::::::::::I'm not sure why we keep going on circles here, but it is abundantly clear what the producers intentions are, every single instance of the film's name on the producers own website has "about" capitalized. This is not an argument by google or argument by popularity, this is how the producer of the films website consistently spells the name of the film (just because I used google as a tool to search their website doesn't invalidate the information I got from the search tool). No style guide can override what the producers of the film intend the title to be, and that is "10 Things I Hate About You". If there was any confusion in the production company then you'd think there would be one single instance of "about" being lowercase, but I haven't found one, and you haven't produced one. It seems to me like a consistent effort has been made to consistently capitalize the name of the film by the production company (and by everyone else too). Your conjecture that the production company doesn't care about the capitalization is not backed up by any facts whatsoever, while I've have provided overwelming evidence to the contrary. 
 ::::::::::Regarding Amazon.com, I'm not sure why we would want to rename the Amazon.com as that is what Amazon.com refers to itself as in textual form (while it's graphical logo uses a lowercase a, whenever Amazon.com refers to itself in text form the a is always uppercase, for example at the bottom of www.amazon.com we see the text "© 1996-2006, Amazon.com, Inc. or its affiliates"). While on Wikipedia is it impossible to have the name of an article be in lower case due to technical restrictions, there are several examples of articles where the subject uses an initial lowercase letter. What Wikipedia does in this case is to put a little note at the top of the article stating that the first letter should be lowercase but isn't due to technical restrictions, see IPod and Id Software. Every reference to the subject of the article in the main text then uses a lowercase first letter. This is only one more argument why the title of the film should be respected according to the producers wishes: Wikipedia already respects the names of products, companies, etc when their first letter is lowercase even though every style guide (including CMS, MLA, Fowlers, and the two I linked to) would most likely say that the first letter should always be uppercase (and it does all this despite the technical restrictions as well). There are tons (almost 1,000) of examples of similar articles in Category:Article titles with lowercase initial letters. 
 ::::::::::When the Wikipedia manual of style says that when all else fails issues should be resolved with a style guide, such as CMS or Fowler's, that most certainly does not mean that CMS or Fowler's should be taken to be the bible of style guides. My understanding of that section is that if the Wikipedia manual of style does not specify a preference on the matter you can consult a style guide, and then it gives some examples of ones to consult. Anyways, this is really moot, as the producers have a clear preference for the title of the film, style guides don't override that. 
 ::::::::::Wikipedia is not an academic journal, it is not a thesis for a university, and it is not a paper for a university course in the humanities. Plain and simple Wikipedia is not part of the academic humanities. I don't think we would see an article on the Symmetric hypergraph theorem in the humanities. 
 ::::::::::"Alan Smithy" is different from "Alan smithee" and "10 Things I Hate About You" is different from "10 Things I Hate about You". So why should only spelling be respected but when a consistent effort to keep the capitalization consistent it should not be respected? Spelling and uppercase/lowercase are just two parts of the same thing. 
 ::::::::::Your "agrument by popularity" point can just as easily be countered by an "argument by emperors new clothes" point: just because someone important says it doesn't mean it's true.