To work around this issue you need to think outside of joomla. Here is what I did.
1) Created a new module using mod_html
2) Noted down the id of the module.
3) Logged in to the backend mysql database and put the adsense code in the module I just created. This way I bypassed all the filtering.
use <joomla_database> ;
update jos_modules set content = '<script type="text/javascript"><!--
google_ad_client = "pub-xxxxxxxxxxxxxxx";
google_ad_slot = "xxxxxxxxxxx";
google_ad_width = 180;
google_ad_height = 150;
//-->
</script>
<script type="text/javascript"
src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
</script>' where id = <module_id> ;
Just remember not to edit this module again from Joomla!