Can't speak to the King's actual thinking, but that issue is somewhat discussed in the US Supreme Court case Johnson v. M'Intosh, which expounded the "Discovery Doctrine," under which it was understood that the natives only had a right of occupancy while the European nation that "discovered" the land gained allodial title.

The case: https://supreme.justia.com/cases/federal/us/21/543/case.html

A Seton Hall Law Review article rejoinding some of Chief Justice Marshall's claims in the Johnson opinion: http://law.shu.edu/Students/academics/journals/law-review/Issues/archives/upload/watson.pdf