Your usergroups where not the default phpbb3 groups from a fresh install. Your groups where like 4860 and above which was a little strange.
I deleted all your groups and refreshed them to make sure all the right groups are right. You will have to reset usergroup permissions.
You can reset your category permissions and then give things a try as I modified your integration file to look for your guest usergroup of 4860 not 1 which is a fresh phpbb install.