LOL. Turns out that it is the HTML after all. Some of that extra code is invalid. The paragraph and div inside it aren't nested properly and so the browsers are closing the paragraph tag themselves, creating an empty paragraph that nevertheless has height. This is the space that you don't want.
Here's what I'd recommend changing your code to produce
Code:
<!--// bof: mysidebox //-->
<div class="rightBoxContainer" id="mysidebox" style="width: 151px">
<h3 class="rightBoxHeading" id="mysideboxHeading">Stuff</h3>
<div id="mysideboxContent" class="sideBoxContent">
<a target="_blank" href="http://link/">
<img alt="stuff" title="stuff" src="http://www.thingy.com/foo.gif" />
</a>
</div>
<!--// eof: mysidebox //-->
and then add the following to your stylesheet
Code:
#mysideboxContent {text-align:center}
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