1. A method comprising a data processor of a file server executing computer instructions stored on a non-transitory computer-readable storage medium to perform the steps of: (a) accumulating quota usage of files in a directory tree when scanning the directory tree and a network client has concurrent write access to the files in the directory tree and changes directory structure of the directory tree; (b) marking each file in the directory tree as checked for quota usage when the quota usage of said each file is accumulated, and inspecting the files for checked status during the scanning of the directory tree so that quota usage of checked files is not accumulated more than once during the scanning of the directory tree; (c) in response to a rename request by the network client to rename a specified file concurrent with the scanning of the directory tree when the rename request specifies a destination directory that is found to be marked as checked, accumulating quota usage of the specified file; (d) restarting a scan of a modified directory in the directory tree to accumulate quota usage of files in the modified directory when the concurrent write access of the network client has modified content of the modified directory during the scan; and (e) using the accumulated quota usage from the steps (a), (c), and (d) to set quota running counts maintained by a file system manager in the file server and used by the file system manager to deny a network client request that would cause a quota running count to exceed a quota limit.