Yes that is a bug .... looks like a very old one as well (the white screen was a bug as well)
Honestly those profile links should not be enabled if you can't view the profile, seems a bit silly to supply a link only to respond with a "you can not do that" ... perhaps something for 2.0
For 1.1.x .... in Profile.controller.php
// No menu means no access at all.
if (!$this->_profile_include_data || (isset($this->_profile_include_data['enabled']) && $this->_profile_include_data['enabled'] === false))
// No menu means no access at all.
if (!$this->_profile_include_data || (isset($this->_profile_include_data['enabled']) && $this->_profile_include_data['enabled'] === false) || !isset($this->_profile_include_data['function']))
I do not think that will have any side effects and will provide the "you can't access that section" message. Not great but better than nothing!