Hello, enenre - and welcome to English Forums. It is an idiom, and you are right as to its meaning, although 'full control' could be considered a usual consequence of 'full access': have the run of swh to be allowed to go anywhere in an area The children had the run of the farm all week. have the run of ( idiomatic ) To have permission or freedom to move around throughout an area or to use at will .
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