An apparatus comprises a host device configured to communicate over a network with a storage system comprising a plurality of storage devices. The host device is further configured to execute multiple processes that generate input-output (IO) operations for delivery to the storage system. The host device comprises a multi-path input-output (MPIO) driver configured to store for each of one or more of the storage devices information specifying one or more of the processes executing on the host device that are permitted to access that storage device, and for each of at least a subset of the IO operations, to determine the particular storage device to which the IO operation is directed, to identify the process that generated the IO operation, and to control delivery of the IO operation based at least in part on whether or not the stored information indicates that the identified process is permitted to access the particular storage device.