Presto agitato: What Might It Mean?

In The New York Times of Wednesday, July 17, 2013 I read in a music review by Zachary Woolfe:
"...his control seemed to wane only slightly in the [Moonlight Sonata]'s finale, when the beat should underlie even the most furious passages."

Really!

Here is an example of how recordings have come to "be" the music.  You can listen to as many recordings as you can readily find of this great work without finding one that seriously questions the meaning of either word, "presto," or "agitato."

But there is plenty to question:  Presto does not necessarily mean as fast as possible.  It might indicate a tempo set by the smallest note value, a meaning consistent with Beethoven's other uses of the term which are, by the way, infrequent.  (In one piano sonata he uses it clearly ironically: "Presto a la tedesco," i.e.. Presto in the German manner, which must mean not fast at all.)

Agitato cannot mean fast: There are many more accurate indications of speed that Beethoven would have used, according to Koch's Lexicon, a 19th-century musical dictionary.  I observe agitato to indicate the pronounced presence of 3's within a duple meter.  Why else would Beethoven so clearly distinguish between the arpeggiated sixteenth-note figures when they appear in sets of 27 (count them!) as opposed to 28 notes?

My question to Mr. Woolfe: If someone were to play the movement in a true agitato would you even be able to take it in or would your only recourse be to listen comparing it to recordings you know and love so well?

I played The Moonlight Sonata in a series last year and one musician's reaction was that he had never heard it played so fast.  Interesting.  It was not, metronomically speaking, fast at all.  Being agitato it felt fast.