This isn't about animate/inanimate. Animate is pod mužem/ pod muže. Also not the same.
It is the basic distinction between a location and direction that is important in most indo-european languages. Latin had separate cases for these, German does today.
It is like here vs. hither.
Right. Before I added "He stood", only "He [has/had] stood" had been allowed. And since you entered "He stood", Duo tried to find the closest correct answer to what you entered. The closest happened to be "He'd stood" but since Duo apparently has some weird long-standing issue with apostrophes, it showed you "Hed stood" as a suggestion of a correct answer. Mystery solved :)