Yohei: Looks like is the vital point. If the liberty at the marked point was filled, then instead of white could play , black , white .
Not sure whether here is considered correct. Up to black is locally dead, but he can escape to the right. In any case, the first diagram is clearly better since black is alive with points. If white cannot permit black to escape in this diagram, then white can make sente seki with at and at .