I don't think anyone has ever suggested that Shakespeare made up the plots of most, or even any, of his plays. (That's one reason why modernised versions which throw overboard the language and keep the plots are really rather a pointless exercise. Or rather, whatever point they have is nothing to do with Shakespeare.)

As Kipling wrote in respect of another storyteller:

When 'Omer smote 'is bloomin' lyre,
He'd 'eard men sing by land an' sea;
An' what he thought 'e might require,
'E went an' took, the same as me!