Oxfordians would like you to believe this canard. It is completely untrue.
The lack of a complete recorded biography for William Shakespeare is disappointing, but not a reason for disbelieving the records we DO have. It is a reason for additional research, and the drawing of educated conclusions about the man’s life, but it is not a basis for disattributing what the contemporary record evidence establishes he did.
The argument is bass ackwards. Authorship is established by evidence of authorship, not by the rest of the biography. If the biography indicated something that disqualified the person as author – an inconveniently timed death, for instance – that would be different. But nothing known in Shakespeare’s biography is a disqualifier from authorship. That we do not have a document stating Shakespeare went to grammar school is not the same thing as saying Shakespeare did not go to grammar school. You need to look at the rest of the evidence. Similarly, that we do not know how Shakespeare learned certain things, about Italy, or nobles, or law – and what he Knew is often overstated – does not mean he did not know those things, merely that how he came to this knowledge – readily available at the time, by the way – is shielded from our eyes.