On a Reforger back in the 80's we had a Blazer go rolling down a huge hill sideways with a case of M203 grenades in the back. While the officers were measuring turds we just went and unloaded it - six rolls being nowhere near arming the damn things. Good times.
Old wives tales.
The number of revolutions is moot, it is the centripetal force generated by the rotational velocity that arms the fuze- think spring loaded pins with a locking mechanism, once the round is spun so fast, the pins slide outwards, lock and the fuzes FP is then free to strike the detonator upon impact.
37 rotations is a fairy tale. However, it indeed takes about 25 m worth of time/rotation to retract the safety pins and lock, so that is the “arming” distance”. Good thing, as the blast radius of the 40mm HE round ( used to be anyway) is 5 m, so you want the round to be friendlyy safe a bit downrange.
Specs on newer rounds may have changed since my time as a Grenadier.
Regarding putting a round through a window at 150m- even the old M203 with folding sights could get that done- if the gunner actually knew how to shoot- all of the fundamentals of marksmanship come to bear.