I'm pretty sure that Tie::CSV gets this wrong, unfortunately - I've tried to use it in the past, and never had much success. However, Text::CSV has worked for me with this type of file (well, Text::CSV_XS, which should be the same thing ;)

The basic loop structure that I have is something like:

my $csv = Text::CSV_XS->new({'binary' => 1});
my $current_line;
while (<CVSFILE>) {
    $current_line .= $_;
    next unless ($csv->parse ($current));
    my @row = $csv->fields();
    $current = '';
    # do stuff with the rows...
}
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This seemed to hold up against some really bizarre files (very _very_ big files, for example), so it looks pretty good. Strangely, I think Tie::CSV uses the Text::CSV module to read lines in, but I don't think it gets the loop right (like above). However, this might be my memory playing tricks.