Icons of beta sites are different form the icons given in the http://stackauth.com/1.0/sites . As example:
Original icon of the English Language and Usage is
where http://stackauth.com/1.0/sites gives the icon
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As Dan Dumitru just pointed out (+1) the varying per site icons have just been implemented indeed, see Would it be possible to get different favicons per beta site? (an extremely welcome improvement btw.!).
In addition George Edison already asked for the respective change regarding the API as well and Jeff Atwood
confirmed this to be worked on already acknowledged this, see Would it be possible to get different “apple-touch-icon”s per beta site?.
Good catch! I'd hope this is something to be resolved soon (i.e. carried over to the API), as the new icons seem to be in place since yesterday only or so - at least I recall looking at my accounts tab several times within the last days (including yesterday) and would swear the beta site icons all looked the same back then still.
Either way this is another indication that the respective API entities don't seem to be simply retrieved from the same backend data tiers like the site entities, which, while not surprising and understandable for more complex topics, still isn't exactly a sign of a mature backend architecture either.
Admittedly the Stack Exchange team is moving quite fast in times, making things like this difficult: I'm regularly impressed by their quick turnaround times on bugs (that is, if they take note of them at all in the first place ...) and sometimes multiple daily releases accordingly.
The change was made only about 5 hours ago:
Not even stackexchange.com has the new icons - http://stackexchange.com/sites - so I suspect it's a thing that will get fixed pretty soon.
These should now be in sync.
Our designer got caught up on inbox stuff for a little bit, sorry for the delay.