Each router checks its table for the destination, and if it doesn't know it, queries the next upstream router, its default route, the next hop. Each router likely ultimately informs you of the hand-off via a packet of some sort, and your then traceroute sends a ping/ICMP to each hop to learn how far away they are.
He maybe could've been pushed to expand on what he did know in more detail, but it seems like she just threw out SNMP as misleading bait, and he maybe mixed up ICMP and SNMP. She is right to call herself a troll, but wow, that's crazy to say she caught the guy in a lie of insanity.