The way I heard it....Eliz the 1st was away at a boarding school or something. She got really sick, so her family was notified. Before her father, King Henery the 8th got there, she died. Henry had a bad rep for flying off the handle, so the matron (in fear for her life) searched the countryside for another girl of the same appearance and stature, to "replace" Liz. None to be found, but there was a boy that fit the description.
Henery wasn't the best of fathers, and had never paid much attention to his children, so when was presented with his "daughter", he wasn't familiar enough with her to know the difference.
The rest....is history.