I had to read the relevant sections three times to sort this out. I believe what they are saying is that this service they made had to speak HTTP in some specific way, and since Redis doesn't speak that way directly they would have needed to proxy requests in their service to Redis which would mean one network hop to reach their HTTP service plus one hop to reach Redis.

Of course, Redis and Memcached support Unix domain sockets which do not use the network and do not suffer from the overhead of TCP. The authors do not address this at all, suggesting they weren't aware of UDS, nor the fact that TCP within one Linux host does not touch the network at all.

Adding to the confusion is that even given an in-memory cache library which overcame their objections to the "network" based ones, they still elected to write their own low-level cache.

So the comment about time needed on the network was either spurious or misinformed. And one thing it was not: measured.