I am not convinced it has anything to do with the permissions on the file or directory.
From the paths used in the original post, it is not a Windoze machine, so with a little cut'n'paste from a Mandrake box:

__PASTE-ONE__
~/temp/graq> ls -l
-r--------   1   graq   graq   7 Oct 24 15:50 Testing.txt
~/temp/graq> cd ..
~/temp> chmod 100 graq
~/temp> perl relpath.pl 
graq/Testing.txt: Permission denied
__END__
[download]

So the error is Permission denied for a file with permission problems.

__PASTE-TWO__
~/temp> cat relpath.pl 
#!/usr/bin/perl -w
use strict;

my $file = 'graq/Testing.txt';

open( TESTING, ">$file") or die ( "$file: $!\n" );
print TESTING `date`;
close TESTING;
__END__
[download]

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