The link you provided is based more for a preference center/subscription center submit. If what you are looking for is a simple URL that unsubscribes anyone that is added via a parameter, you should instead look at the web collect form.
The web collect form allows you to manipulate the status of a person on All Subscribers via the 'sub option. You will need to have your List ID for your all subscribers list - which can be found in UI under the 'properties' tab of All Subscribers.
If you do not want it to redirect (default to redirect to success or failure page) and/or you want it to auto-submit - you will likely need to use Javascript and AJAX to manipulate the posting.
Example script from website:
<form action="http://cl.exct.net/subscribe.aspx?lid=YOUR LIST ID HERE" name="subscribeForm" method="post">
<input type="hidden" name="thx" value="YOUR THANK YOU PAGE HERE" />
<input type="hidden" name="err" value="YOUR ERROR PAGE HERE" />
<input type="hidden" name="usub" value="YOUR SUCCESS UNSUB PAGE HERE" />
<input type="hidden" name="MID" value="YOUR MEMBER ID HERE" />
<table cellpadding="0" cellspacing="0" border="0">
<tr>
<td><font face="Verdana" size="2">Name:</font></td>
<td><input type="text" name="Full Name" /></td>
</tr>
<tr>
<td><font face="Verdana" size="2">Company Name:</font></td>
<td><input type="text" name="User Defined" /></td>
</tr>
<tr>
<td><font face="Verdana" size="2">Email:</font></td>
<td><input type="text" name="Email Address" /></td>
</tr>
<tr>
<td><input type="radio" name="Email Type" value="HTML" checked="checked" />
<font face="Verdana" size="2">HTML</font>
</td>
<td>
<input type="radio" name="Email Type" value="TEXT" />
<font face="Verdana" size="2"> Text</font>
</td>
</tr>
<tr>
<td>
<input type="radio" name="SubAction" value="sub_add_update" checked="checked" />
<font face="Verdana" size="2">Subscribe</font>
</td>
<td>
<input type="radio" name="SubAction" value="unsub" />
<font face="Verdana" size="2">Unsubscribe</font>
</td>
</tr>
<tr>
<td>
<input type="submit" value="Submit" /></td>
<td align="right">
<font face="verdana" size="1" color="#4C5487">
Powered by<br> <a href="http://www.exacttarget.com">
<img src="http://www.exacttarget.com/gfx/smalllogo.gif" border="0"></a>
</font>
</td>
</tr>
</table>
</form>