I think it is assuming "$_" as the entire current line of the file.

No. At least in recent Perls (I am using 5.12) the $_ used in grep is localized and contains in your example the current element of the array - your code is ok here.

You can easily verify that yourself if you add a trace, e.g:

... grep {print STDERR "\$_: $_\n"; $_ eq $arrList[2]} @list_match
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So whatever the problem is, it is not a collision of $_.

btw: I would use a variable when looping through a file, instead of using $_:

while(my $line = <INPUT>){
 chomp($line);
 ...
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Then you don't have to worry about $_ getting clobbered by something else and you code becomes more readable.