I think everyone should take a look at the Wikipedia article for theories of who actually wrote the works penned to name "Shakespeare" (https://en.wikipedia.org/wiki/Shakespeare_authorship_questio...) and scroll down to the "Alternative Candidates" section. When you read one, the circumstantial evidence looks perfect. Then you read another candidate and you say "gee that sounds really valid too...". Obviously they can't both be right, but each one presents circumstantial evidence that seems to connect perfectly.
After you've red the alternative candidates, read the "Case for Shakespeare's authorship", which is the case that it really was Shakespeare of Stratford-upon-Avon that wrote the plays. There's some hard evidence (though not enough to be 100% conclusive, it's probably 90% conclusive, and enough convince most scholars) that makes the rest of the theories seem totally unfounded.
I went on a bit of a rant here, but hopefully my point comes across, that circumstantial evidence is really quite far from real hard evidence. Unless some guy comes forward with those bills with the correct serial numbers or someone finds a body, it's going to remain an unsolved mystery.