A string which is (possibly) interpolated and then executed as a system command with /bin/sh or its equivalent. Shell wildcards, pipes, and redirections will be honored. The collected standard output of the command is returned; standard error is unaffected.
Given the bold statement, I call "bad design" on the last phrase. This has been very frustrating. Perl's philosophy of sometimes guessing what I mean rather than taking what I say at face value has now officially really ticked me off. At the very least, this construct should produce a warning message!
The documentation is correct. The backticks execute /bin/sh and capture the STDOUT of /bin/sh. the string you specify, including the redirection, is processed by /bin/sh -- perl (and hte backticks) don't know or care that you have asked /bin/sh to execut "cmd" and redirect cmd's STDERR to cmd's STDOUT (which then becomes the STDOUT of /bin/sh). All perl does is is take /bin/sh's STDOUT and give that to you.
See the previous comments explaining why it doesn't seem like it's working because of your flawed test case
The example you said does work would also appear to fail, if you had written it to work the same way (ie: print in single scalar variable in which you have slurped all of the data from F)