If the HBC uses IOS36, you can just install the most recent non-fakesigned IOS36 and it should work. But having a patched IOS36 is something some people want to keep, so generally the norm is to install IOS61, then run the hackmii installer and reinstall the HBC (to use IOS61). A clean IOS34 is also installed so that the hackmii installer doesn't give you the "no vulnerable IOS" error.
edit: I just saw your edit, and what wiipower is referring to is the same no vulnerable IOS error I mention above. The norm is to install a non-fakesigned IOS34 to get past this error, but many other non-fakesigned IOSs can also fix the problem (you only need @ least ONE vulnerable IOS to run the installer). Most people only run into this problem if they have or had an older version of cIOScorp installed at one point (without properly uninstalling it).
edit2:The hackmii installer tries each of your IOSs in some kind or orderly fashion, and once it finds one to run the installer, that IOS is used to run the installer. The same thing is done when installing the HBC, but I know that it will always try to install to IOS61 first if it is found on the system, and I'm pretty sure IOS36 is the second choice.