Or, slower (no short-circuit) but shorter:

foreach $row (@{$list}) {
    my @matching = map {
        String::Approx::amatch($row->[$_+1],$vals[$_]) ?
            $_ : ()
    } (0..$#vals);
    return (@matching==@vals) ? $row[0];
}
# none found; do the insert, get the new id and return it
[download]

(no check for undef columns here either...)