Knowing, no. But as I was just discussing with another person, in those days they had no idea what caused disease, and they sure didn’t know the blankets had anything in them to cause smallpox. The more I think about it the more I think they probably didn’t know if the Indians suffered from smallpox before the British got there!
Miasma theory predated germ theory. We’ll always have a theory. We may not be right, but we’ll always have a theory.