Chris Li has already pointed out that the "translation" that John Stevens rendered from O'Sensei's writings was not accurate. A more accurate translation was provided which actually supported the position that Dan put forward. Another interesting question is why Saito Sensei did not publicly correct this translation? Or why Saito Sensei did not work off of the more accurate description (six directional awareness) when he was teaching particular stances?
In Saito's commentary to "Budo" he correctly notes that O-Sensei used "six-directions" and not "hanmi" or "60 degrees", but he speculates that this is because O-Sensei did not use the term "hanmi" at that time budo was written (for some reason unspecified by Saito).
My personal hunch is that it's one of those things that O-Sensei dropped because nobody understood what he was talking about and he didn't care to explain - for all that he broke with Takeda it seems to me that he was somewhat cagey about stating some things explicitly in clear language. Many times it seems that he expected (or wanted to see) people following the hints he dropped - also a common traditional tactic. "Stealing the techniques", in other words.