This latency requirement primarily applies to Raft protocol communication between servers within a Consul datacenter. Higher latency values could affect the availability of cluster. See the server performance page in the Consul docs for variables that can be tuned to potentially allow for more latency between server agents.
Consul clients can likely operate at higher thresholds than servers. We are in the process of determining a reasonable latency ceiling. We will update our documentation with this information once that range has been determined.