Yes, it can be done, although the procedure is far from trivial:
"Load" your unbootable HKLM registry hive from your bootable machine:
a. In regedit, select HKEY_USERS and do
File|Load Hive in the menu.
b. Select X:\Windows\System32\Config\SYSTEM file (of course replace X: with your actual broken Windows boot disk letter).
If you cannot load that file because of permissions, you'll need to take ownership of it, apply more relaxed permissions (I'd say word readable/writable so your original Windows will still be able to access it for sure). Remeber to fix the permissions back later when you boot into your fixed OS.
Read more about registry hives on Microsoft web site, if needed.
Fix the problem:
Once you loaded the SYSTEM hive of the broken Windows, follow the steps in the article you mentioned to fix the problem you created. You might have problems with registry permissions. If in doubt, better give more relaxed read permissions so your broken Windows can read that key for sure.
In conclusion, the whole process is doable, but if you're not careful (mess the permissions on the loaded hive for example), you might end up with worse situation than where you started. So beware.