One thing I can think of, although it seems weak, is access () uses real, not efficient uid and gid. This presumably allows you to use the setuid program (which runs as a regular user, but which gets owner permissions) to check if the caller can read the file, to prevent that user from unintentionally granting access to a file that they cannot read, possibly using some symbolic link or hard link trick. I cannot find any evidence that this is possible, or that this is not possible with stat (), but imagine this scenario:
user executes program program is setuid, immediately gets all privs of root program checks file1 to ensure that user has access file1 is a hardlink to file2, which user has access to user changes file1 to hardlink to file3 (/etc/shadow or something like that) program reads file1 and does something to it (print, convert, whatever) user now has access to a file they shouldn't
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