This is NOT a problem, so there’s no need to worry. The router is behaving normally. The fact your router is addressable via its public IP does NOT necessarily mean its remote administrative interface is open and accessible to the Internet at large.
Your router always has two IP addresses by which is can be addressed; the public IP (assigned to the WAN) and the local IP. It has to, it’s a router, it straddles both networks and routes between them. The mistake by the OP is assuming the mere fact someone uses the public IP indicates the direction of access. It doesn’t. That’s determined by the router by examining the IP address of the device that’s attempting to access it! If it’s a local IP address (i.e., behind the router), access is always permitted (assuming a valid logon is provided). If it’s a public IP address, access is denied (by default) unless remote administration is enabled (again, assuming a valid login is provided). IOW, it’s the originating IP address that’s determinative, not the destination IP address.
Based on this knowledge, it should now makes sense why there’s no way to determine if your router is remotely accessible short of actually attempting access from the Internet side of the WAN. The router is perfectly happy to allow anyone w/ a local IP address to access it, regardless whether they specify its local or public IP. However, go to a friend’s house and have the router see your public IP address, and it’s a different story. Now it refuses (unless you’ve enabled remote administration).