@bholman, thanks for posting a link to the live example. I made a video http://www.screenr.com/bzqs which explains the reasons why your theme has underlined links in some cases but not other one.
I ran out of time trying to explain how the <div class="content">...</div> wrapper could've been added... basically, widgets have placeholders $before_widget, $after_widget - this placeholders are being utilized by themes to wrap widgets into their own tags. Some themes utilize
tags to wrap widgets, others divs with specific classes. If a widget author doesn't include those placeholders (which is a good practice and official WP Codex teaches to include them), then the widget will not have those wrappers. In my case I did include them, and my widget does obey by the Theme's style rules.
If you wish to avoid any bordering on the links, simply overwrite your existing rule with:
body .content a:link, body .content a:hover, body .content a:visited {
border: none;
}
add that at the bottom of your theme's stylesheet and I think it should be sufficient. If not, then you'll have to use the element inspector to nail down all the rules that affect those links.
Anyway, I just hope this gives other users an idea on how they can fix this type of issues.
P.S. if you open up the main PHP file of the plugin and simply search for class or even word "content" within the code - you won't find it. So, again, the class is not being added by the widget itself.