You need to add escape_char => q{'} or somesuch, otherwise the quote marks are treated as escapes. In the next release I intend to have the escape_char default to whatever the sep_char is set to rather than to " as it is now. This parses your sample correctly for me:

#!perl -w
use strict;
use Text::CSV_XS;
use IO::Scalar;
my $str = q{'title'|'Some Name, "some wierd title"'|'555-555-5555'};
my $csv = Text::CSV_XS->new( {
    binary=>1,
    quote_char=>q{'},
    sep_char=>q{|},
    escape_char=>q{'},
} );
my $fh  = IO::Scalar->new(\$str);
while (my $cols = $csv->getline($fh)) {
    last unless @$cols;
    printf "%s\n", join "\n",@$cols;
}
[download]