Casella & Berger state Basu's Theorem (Th 6.2.24) as follows:
If $T(X)$ is a complete and minimally sufficient statistic, then $T(X)$ is independent of every ancillary statistic.
However, in lecture, I saw a proof of the theorem that used only sufficiency, not minimal sufficiency. The proof was basically an application of the law of total probability.
Wikipedia states Basu's Theorem using sufficiency and bounded completeness (a weaker requirement than completeness), which agrees with my lecturer.
What gives with the Casella-Berger version?