Why are researchers at some think tanks titled professor? Within my own discipline one of the best examples of this may be at the Santa Fe Institute, but I've seen this other places as well. Quite simply, why are researchers at some think tanks titled "professor" when they don't have a university affiliation?
The word "professor" is most often used by universities, but the content of the word more generally refers to a person whose job is some mixture of higher-level education and research.

Thus, while it is unusual for a place like the Santa Fe Institute to call some of their employees professors, I would judge it to be a reasonable description of their work given that the institute is well-respected in the academic world as both an educational and research institution.  

Most other industry or "think tank" organizations do not have a similar mission and it would thus be less appropriate for them to give such a title to their staff.