I do believe it was a stranger. JonBenet was little Miss Colorado and appeared in a pre Christmas parade shortly before her murder riding on a float with her full makeup on. She was a pedophiles' dream and there were so many registered sex offenders in the area as well as those whose tastes ran to pedophilia. There was a broken window in the basement of the Ramsey home which would have provided entry for a killer and shrubbery outside to provide cover.
Perhaps any resemblance between Patsy Ramsey's handwriting and the ransom note was coincidence. It wasn't enough to convict any of the Ramsey's of the crime or even to imply complicity.