I hope you're still following this thread, because I just realized a better way: Test STDOUT, not STDIN. You don't care where the input is coming from, but whether you are outputting to the screen or to a file.

$ cat works.sh
#!/bin/sh
perl -le 'print "Screen" if -t STDOUT'
perl -le 'print "File" unless -t STDOUT'

$ sh works.sh
Screen
$ sh works.sh > out.txt
$ cat out.txt
File
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