Linux – Inconsistent behavior of `w` command concerning `WHAT` column

On linux at least, since any user input on the terminal will access the current user device it does a stat() call to /dev/{tty,pts/}?* and checks for atime for logged in users.

From w.c:

    /* stat the device file to get an idle time */
    static time_t idletime(const char *restrict const tty)
    {
            struct stat sbuf;
            if (stat(tty, &sbuf) != 0)
                    return 0;
            return time(NULL) - sbuf.st_atime;
    }

    static void showinfo(utmp_t * u, int formtype, int maxcmd, int from,
    ...
            print_time_ival7(idletime(tty), 0, stdout);
    ...

stat() only requires execute (x) permissions on parent directory to work.

As explained in other answers and comments the reason for what you observe is the way Bash handles pipes. In order to filter what you really want in similar situations you can try to enclose the first letter of the grep argument in [] like this:

$ strace w 2>&1 | grep random
read(4, "grep\0random\0", 2047)         = 12
$ strace w 2>&1 | grep '[r]andom'
$ strace w 2>&1 | grep '[c]lose'
close(3)                                = 0
close(3)                                = 0
close(3)                                = 0
close(3)                                = 0
close(3)                                = 0
close(3)                                = 0
(...)

EDIT:

As correctly noted by R. in the comment below in fact strace does not see the other side of the pipe. Similarly to ps aux | grep grep which also shows grep grep in its output w is is walking through /proc directory and finds grep process there.