1. A storage system, which receives an I/O (Input/Output) request specifying a logical address of a logical storage area from a higher-level apparatus, comprising: a RAID (Redundant Arrays of Inexpensive Disks) group comprising multiple physical storage devices; and a storage controller, which, in accordance with the I/O request from the higher-level apparatus, configured to send an I/O command to a target physical storage device, which is an I/O-destination physical storage device in the RAID group, each physical storage device comprising: a physical area, which is regarded as the basis of the logical storage area; and a device controller, which is coupled to the physical storage area, configured to execute internal processing, which is processing executed without receiving a command from outside of the physical storage device, wherein a physical storage area state changes in accordance with the input/output of data to/from the physical storage area, the device controller inside the target physical storage device is configured to: (a) execute data I/O processing with respect to the physical storage area in accordance with the I/O command from the storage controller; and (b) subsequent to executing the I/O processing in the (a), send to the storage controller a response with respect to the I/O command, the response comprising status information, which is information denoting a state of the physical storage area subsequent to being changed in accordance with the I/O processing, the storage controller is configured to: (A) receive the response from the target physical storage device; and (B) based on the status information included in the response received in the (A), make a determination as to whether or not to execute the internal processing, and in a case where the result of the determination is to execute the internal processing, send to the target physical storage device an internal processing execution command instructing to execute internal processing, and the device controller in the target physical storage device is configured to: (c) upon receiving the internal processing execution command, execute internal processing in accordance with the internal processing execution command, wherein the status information is information as to whether or not the target physical storage device is in a state in which the internal processing is necessary, wherein the storage controller comprises a storage area, and the storage area stores management information comprising information denoting whether or not respective multiple physical storage devices are executing internal processing, and wherein (Y) the storage controller, in a case where a read request has been received from the higher-level apparatus, is configured to send a read command for reading read-target data to a read-source device when the management information denotes that the read-source device, which is the physical storage device constituting the destination of a read command conforming to the read request, is not executing internal processing, and, when the management information denotes that the read-source device is executing internal processing, perform a correction read in which read commands for reading data and parity are respectively sent to multiple other physical storage devices of the RAID group to which the read-source device belongs, and the read-target data is restored based on the data and parity read in accordance with these read commands.