In IPv4, ICMP is used to send TTL exceeded messages regardless of what upper level protocol was used in the packet that expired in transit. UDP, TCP, ICMP, doesn’t matter.
The slides you linked to are correct, in general, about router slow path behavior, but that isn’t what makes UDP ping “more reliable”. It’s “more reliable”, theoretically, because UDP is less likely to be subject to indiscriminate filtering than ICMP.
Additionally, generally only ICMP sent to or generated from a router goes through the slow path. An IP packet being sent through a router generally goes through that device’s fast path, regardless of the payload type.
We're not disagreeing with the presentation, you're misunderstanding it.
No matter which protocol you use the packet only has one destination, the destination IP, so it does not go through the slow path on any hop on the way just because its ICMP. When a packet hits the TTL limit on a hop it will go through the slow path as the CPU will generate the response ICMP. The protocol used for traceroute makes no difference here.
