When PATH is used to locate a file for the dot utility[1] , the file's readable bit has to be set. The executable bit is not important. The POSIX shell ignores non-readable files.
When PATH is used to locate a file for the dot utility, the file's readable bit has to be set. The executable bit is not important. If file is executable and not readable, then the interactive shell displays a diagnostic message to standard error, and the non-interactive shell aborts.
[1] | dot is a special built-in utility |