Common misconception.
If you look at how the starter solenoid is constructed, the starter motor cannot get power--and therefore cannot spin--unless the solenoid plunger is magnetically drawn-in.
And if the solenoid plunger is drawn-in...the starter drive pretty-much HAS to be engaged with the flywheel. Even with the shift-fork worn, the drive will be shoved into the flywheel/flexplate ring gear.
When the starter motor spins, but the engine doesn't crank, it's virtually guaranteed that the starter drive is engaged, but the one-way clutch is slipping.