First of all, not having backups should, IMO, be a firing offense. No second chances.
That depends on the curcumstances. If the box that failed was one of a cluster of many identical ones behind a load balancer, and the suplicant thought that he could rebuild a replacement fairly quickly then it is reasoable not to backup individual boxes, just the configuration necessary to rebuild one.
I am also responsible for a number of production boxes that are not backed up, but they are part of a redundant cluster, and the configuration to build another is in a Puppet server, so if one fails, I can recreate another one in an hour or so.