That's not always true. If you have cable internet service, you can clone the MAC address of your PC on your router and then reboot your cable modem. Due to the MAC address change, you should get a new IP address.
True - and dynamic addresses can always change - my reply was somewhat simplistic. But, in my experience, when an IP address is blocked by a site it is normally a network range rather than a single address. A new dynamic address is still very likely to lie within the same blocked range.
As the OP says, you can certainly change your local IP address (if you have a router and are using NAT), but that's going to have zero effect. It's the public address, the address of your router, that is blocked.