Question from Laura - "Secrets of the Virgin Queen"

I recently watched Secrets of the Virgin Queen on NatGeo, and one of the "secrets" was the discussion of a rumor about "the Bisley boy." I had never heard this before, and I while I think it's clear it's a ridiculous rumor, I'm wondering how many people believed it, and whether it was a rumor known during Elizabeth's time, or did it come from a later era?

The show also claimed that Elizabeth wore her makeup to hide pox scars from a bout of small pox. Is it true that she had smallpox? I've never read that before. I was under the impression that she started using the makeup to hide signs of aging (and achieve the desired pale English complexion), and that the use of the white lead makeup discolored her skin causing her to need to use more to cover the effects.

I've focused most of my reading on Henry and his wives so I'm not as familiar with the rumors and common misconceptions about Elizabeth as I am about those of her mother.