Yes black holes are created by exploding stars, because they leave large holes of very concentrated gases. This also helps explain why the theory of matter being destroyed in a black hole is a fallacy, because the matter is not destroyed, it is just lost in a very concentrated space. Exploding stars have to send their matter somewhere.
As I understand it black holes are created by exploding stars, not a very fast spin. I believe the problem with the fast spin theory is the fact that there's no weight involved and nothing to cause the fast spin in the first place. I find the topic fascinating, but difficult to comprehend.
Exploding supermassive stars collapse upon themselves and form black holes, at least that is the prevailing astronomical theory regarding the formation of super-dense bodies in space that don't even allow light to escape. Black holes emit radio waves at their poles, which is one way astronomers detect them. The radio waves wobble because they are spun at extremely fast rates. Black holes do spin once they are formed, but they don't get that way in lighter stars.
Black holes are created by exploding stars, although it is possible they could be created by a very fast spin too. Black holes are usually created when a big star gets too old, then it explodes. It explodes with such a force that a black hole is created when this happens.
Black holes are a kind of energy that has not yet been able to be explained. So to posit anything absolute is wrong because even the scientists do not know the whole truth. This is an amazing universe with many galaxies comprised of millions of heavenly bodies, but the very fast spin sounds like a better choice.
A fast spin causes a very high inwards equatorial pressure until a latitude of nearly 35°-36°, which counteracts the inertia. At high spin rates, this compression area becomes even independent from the spin rate. And even if their mass is rather limited, their gravity fields become gigantic. That can cause a collapse inside the star.