If you don't create what your $AMPWEBROOT is before running the install (lets take the example of /var/www/html which doesn't always exist, sure /var/www probably does but not all distributions come with a html directory inside that)
Then FreePBX creates it for you! woop woop!
root@underpants:/var/www# ls -lah
drwxr-xr-x 2 root root 4.0K Jun 6 12:51 .
drwxr-xr-x 15 root root 4.0K Jun 6 12:51 ..
drwxr-s--- 6 root root 4.0K Jun 9 19:36 html
Oh dear oh dear...
1) Presuming your web server is running as asterisk:asterisk (as advised and expected) and you point it at that directory it won't be able to read... either (you can pick a reason why) it should be owned by asterisk:asterisk OR! it should have the correct 'other' permissions such as o+r.
2) Lets say instead you point your web server at the admin directory inside that (which is made asterisk:asterisk by the installer correctly) you still won't be able to access it because the parent directory can not be read due to the lack of ownership and/or other permissions.
So _if_ the 'html' (or more officially $AMPWEBROOT) directory is meant to be asterisk:asterisk (presumably so that files in here can be updated by the Framework module) then when the installer makes the directory it should correct the ownership.
Else at the very least it should keep the o+r flag so others who are not the owner of the directory can read past it like the web server.
But I have feeling it is meant to be asterisk:asterisk so if you ever wanted to update the lovely index.html splash screen you could using the Framework module.
I'd provide the fix for this, but I'm struggling to locate it, all I can see is that around line 1100 of install_amp the files/directories get touched as asterisk:asterisk - maybe this would be a good place for the fix?