This is quite common and you are right, its because the DNS hasn't been refreshed and shows the old host name it was initially registered to.
I have a similar case as well. I been allocated a bunch of IPv4 and IPv6 addresses. The IPv6 are natively allocated and will resolve properly in either way (reverse or not). But 5 of my IPv4 were previously used by someone else and he/she used his own DNS servers to resolve them. Now I use them natively. I don't use any registered DNS server to handle them.
So, if you do a DNS look up on my domain name, it will resolve correctly to the IP address but if you do a reverse DNS, it will point to a different domain name.