"Routing" is a rather generic term when it comes to large networks, and everything from border routers, firewalls, load balancers, and switches actually perform routing.
Especially (as I've mentioned in another post) when you add fault tolerance / failover configurations to the mix.
Routing failure doesn't have to be an all-or-nothing thing. There are a number of ways in which I can see ICMP echo packets working but other traffic not, especially when you include complexities of source routing, load balancing, failover, etc.
Even something as "simple" as a poisoned ARP cache in a single box could screw up the entire internal network and cause the problems they've had, and still be considered a "routing issue".
$0.02