The information that you received is oversimplified. Yeast cells do not store O2, they store ergosterol and unsaturated fatty acids (UFAs).
Dry yeast does not require much in the way of dissolved O2 on the initial pitch because it is propagated aerobically below the Crabtree threshold in a bioreactor. All reproduction is via the aerobic metabolic pathway. Ergosterol and unsaturated fatty acids (UFAs) are synthesized in the aerobic metabolic pathway; therefore, the cells go into a fermentation with fully-charged ergosterol and UFA reserves.
Liquid is yeast propagated above the Crabtree threshold, which means that all reproduction is via the anaerobic metabolic pathway. Dissolved O2 along with a small amount of carbon is shunted to the aerobic metabolic pathway for ergosterol and UFA biosynthesis during the lag phase. One of the reasons why we want to pitch a starter at high krausen is to preserve ergosterol and UFAs stores because all replication beyond this point is for replacement only, and mother cells share their ergosterol and UFA reserves with their daughters.
With that said, dry yeast is just like liquid yeast at the end of fermentation. O2 is needed on a repitch to rebuild the ergosterol and UFA reserves that were depleted during replication and fermentation.