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Astrophysical black holes (BHs) can be fully described by their mass and spin. However, producing rapidly spinning ones is extremely difficult as the stars that produce them lose most of their angular momentum before the BH is formed. Binaries where the progenitor is paired with a low-mass star in a tight orbit can produce rapidly spinning BHs (through tides), whereas those with massive companions cannot (as they do not fit in such an orbit). A few rapidly-spinning black holes (BHs) have been observed paired with very massive companion stars, defying stellar-formation paradigm. Models which reduce the stellar-core--envelope interaction (and winds) do not match observations nor theory well; I show they also miss explaining the energetics. BH spins cannot be produced during stellar collapse; using orbital spin through explosion-fallback material does not match the observations; spinning BHs up through accepted mass-transfer channels takes longer than their lifetimes, it is usually discarded. I show that fast mass-transfer mechanisms, predicted to merge the BH and star, successfully spin the BHs up and show a mechanism to avoid said mergers and main dangers of the alternatives while naturally explaining the observations. The implications are potentially paradigm-shifting and far-reaching in the high-energy, BH astrophysics context.