Using HTML::LinkExtractor v.11 from backpan, and the bug previously mentioned, I reproduced the bug, and could not find anything wrong with HTML::TokeParser::Simple(v3.13). I did however find this in HTML::LinkExtractor:

## In case we got nested tags
if(@TEXT) {
    $TEXT[-1]->{_TEXT} .= $T->as_is;
}
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I have some idea of what the purpose of the code above was, but it had the effect of setting the current "text" of the link (even the top level non-nested link tag since the @TEXT array was non-empty and the _TEXT contained an empty string) to the entire <a href="..."> tag (and then later the actual text is appended).