Some massive, merging black holes (BH) may be descendants of binary O stars. The evolution and mass transfer between these O stars determines the spins of their progeny BH. These will be measurable with future gravitational wave detectors, incentivizing the measurement of the spins of O stars in binaries. We previously measured the spins of O stars in Galactic Wolf-Rayet (WR) + O binaries. Here we measure the vsini of four LMC and two SMC O stars in WR + O binaries to determine whether lower metallicity might affect the spin rates. We find that the O stars in Galactic and Magellanic WR + O binaries display average vsini = 258 +/- 18 km/s and 270 +/- 15 km/s, respectively. Two LMC O stars measured on successive nights show significant line width variability, possibly due to differing orbital phases exhibiting different parts of the O stars illuminated differently by their WR companions. Despite this variability, the vsini are highly super-synchronous but distinctly subcritical for the O stars in all these binaries; thus we conclude that an efficient mechanism for shedding angular momentum from O stars in WR + O binaries must exist. This mechanism, probably related to Roche lobe overflow-created dynamo magnetic fields, prevents nearly 100% breakup spin rates, as expected when RLOF operates, as it must, in these stars. A Spruit-Tayler dynamo and O star wind might be that mechanism.