Merry Devil was written in 1603, so goes the theory, and was performed at The Globe, by the King's Men. In an environment where a company could and did edit the text of a play to suit the needs of their performance of it, this almost begs the question: why not bring in your best playwright to make the edits. There's ample evidence to suggest that Shakespeare didn't write The Merry Devil, but at the same time, there's every reason to think that he would have had at least a small hand in revising it to meet the needs of the company. Remember, the script we have is probably a cut version; someone had to do the cutting.
This isn't to say that there is any way to track Shakespeare's hand in The Merry Devil. Nor can anyone actually prove that he had any hand in editing the text, revising the text, or playing in the text. It might have all been done by Cuthbert Burbage, the company bookkeeper. For all we know, Shakespeare had a nasty case of the flu when the company was preparing the play for stage or tour. Or maybe Shakespeare's edits made the cutting room floor. There's just no way to know.
I'm going to lean on the side of Shakespeare's invisible hand guiding the text of Merry Devil, even if it didn't write all, most, or even much of the script. It doesn't really tell me anything useful about the play mind you, but it's nice to think about.