This line of reasoning does indeed embrace an alternate theory, the theory that Shakespeare didn’t write Shakespeare’s plays. And it does so based on an isolate

This line of reasoning does indeed embrace an alternate theory, the theory that Shakespeare didn’t write Shakespeare’s plays. And it does so based on an isolated morsel of circumstantial evidence, just as the OP described. When an argument hinges on the sentiment “it seems unimaginable…” it often means that circumstantial evidence is being recast as something more definitive than it is.