Saying I can only make a claim if I have done a certain study is somewhat absurd, especially when you are, with that suggestion, claiming to be the authority on how to determine what is correct.
And I'm sure if you asked editors at big publishing houses or english teachers, most would tell you to prefer "themselves." Themself is a new construction that hasn't caught on. Purveyors of "standard" English have to err on the side of conservatism.
^^^
Read it for your own good.