The thing is, spin-stabilization of the sort being discussed depends on an atmosphere. What happens is:
1) The projectile leaves the barrel, pointy end aligned with velocity, spin axis aligned with the direction of motion.
2) Turbulence and slight asymmetries apply torque to the projectile along an axis perpendicular to the direction of motion.
3) The gyroscope effect turns that torque into a "sideways" push that makes the point precess slightly around the direction of travel, rather than veering away from it at an ever-increasing rate.
4) Aerodynamic effects tend to bring the body back into pointy-end-first alignment if the perturbations are sufficiently dampened by the gyroscope effect.
The whole thing is a rather beautiful dynamic dance between aerodynamic and gyroscopic effects. In space, nothing like steps 2 and 4 can occur.