I think your guess is right. That is, The definition of Kakeya set is different from that of Besicovitch set.

"Note however that though Besicovitch showed that needles may be turned in sets of arbitrarily small measure, these sets, unlike Besicovitch sets, may not have zero measure."

Also see
http://terrytao.wordpress.com/2008/12/31/a-remark-on-the-kakeya-needle-problem/