Well as far as I can see it's the only way to see if this is a Moodle problem or the Adaptable theme problem.
You can test Clean theme by first selecting Allow theme change in URL which you will find if you navigate to
Administration > Site Administration > Appearance > Themes > Theme settings => Allow theme change in URL
After clicking on the checkbox you need to save settings.
All you need to do then is add ?theme=clean
into the address bar of your browser after the url of your site...for example:
http://bylazydaisy.co.uk/?theme=clean
Only you will see that theme so you can test your site to see if those blocks are being hidden in the Clean theme too.
Hope that helps?