The companies who operate the cross-country backbone fibers have independently verified fibre maps and you can also audit them with their cooperation. And those who operate last-mile metro networks are usually highly reputed ISPs (at least in India where there is decent competition in this space) who have a lot to lose if their reputation is damaged. Also, the community of their customers is small and they all talk to each other. So it is hard to make fake claims and get away with it. Usually, when cable cuts happen, it is more a question of whose traffic is rerouted on the available paths and whose traffic is dropped. If you are high-paying customer with strong SLAs then your traffic is usually safe and will displace a lower SLA customer's traffic. You will notice latency spikes due to rerouting and maybe temporary glitches w.r.t link stabilization. Since you see this so often, your BGP timers etc are all tuned to be patient and avoid cascading failures.