As the title suggests, how do ISPs, and other networks connected to the backbone ensure that their host network address isn't already in use by another backbone node, as there is no controlling device that governs them?
The RIRs assign addressing to the ISPs. An ISP not following the rules will quickly find itself ostracized and cut off from the rest of the Internet.
IANA owns the addressing and assigns each of the five RIRs blocks of addresses, and the RIRs assign blocks of addresses from those to businesses that can prove they need them and are willing to pay for them. At least that is how it worked until IANA ran out of IPv4 addresses, then each of the RIRs ran out of IPv4 addresses. It still works that way for IPv6.
If a carrier gave an IP address to one of its routers which is already used, and announced in the BGP tables, then any traffic for the correct destination travelling through the stolen IP address, will get swallowed up by the errant router. And as others have stated, would get a bit of a slapping.
However, quite a few carriers use private IP addresses, and since they are liable to be re-used, then that could pose a problem. It doesn't however, since they do not announce them. They are used on point-to-point links within the same carrier.
There is another issue though. A UK supermarket decided there were not enough private IP addresses available for their network, so they decided to use another company's public addresses. Not a problem, until we were required to connect to them. The network team ended up having to dual NAT it.