Two popular YouTube gun channels TAOFLEDERMAUS and C&Rsenal teamed up to prove or bust a myth! There is a popular belief that the trench shotguns issued to US troops during the WW1 were not only used for their main purpose of providing a huge firepower when fighting inside the trenches but also were used to shoot down the incoming German “Stielhandgranate” hand grenades (a.k.a. the potato masher grenades).
The Remington Model 10 trench shotgun that Mae of C&Rsenal uses in the video below, was primarily issued with 00 buckshot ammunition, which is not the best choice to shoot flying objects. Birdshot would be better for hitting them. However, not only it has to hit the grenade but also carry enough power to stop it or make it explode in the air.
So, in a nutshell, it is possible, but not with 100% reliability and consistency.
I think it is a less likely scenario that the enemy is at the distance of throwing a hand grenade and you have nothing else to do but skeet shooting grenades. Could it take place? Sure! But I don’t think it was too common. I assume the more common reaction of a soldier seeing a grenade flying in his direction is to find a cover rather than taking the chance of shooting it down.