I think in this case they weren’t talking about the kind of shared-nothing per-request DB connection failing, but a persistent DB connection pool failing to connect during the initialization phase of a persistent app server.
In most runtimes, initialization like that is linear (think bash’s execfail switch); if something fails to initialize, the whole HTTP app daemon will crash out, get restarted by its init(8) process, and then try again.
In Erlang, you’ve got something more like “services” in the OS sense: components of the program that each try to initialize on their own, independently, in parallel, with client interfaces that can return “sorry, not up yet” kinds of errors as well as the regular kind—or can just block their clients’ requests until they do come up (which is fine, because the clients are per-request green threads anyway.) In Erlang, the convention is that these services will just keep retrying their init steps when they hit transient internal errors, with the clients of the component being completely unaware that anything is failing, merely thinking it isn’t available yet.
Certainly, Erlang still has a linear+synchronous init phase for its services—just like OSes have a linear+synchronous early-init phase at boot. But the only things that should be trying to happen in that phase involve acquiring local resources like memory or file handles which, if unavailable, reflect a persistent runtime configuration error (I.e. the dev or the ops person screwed up), rather than a transient resource error.
Indeed, any language runtime could adopt a component initialization framework like this; but no language other than Erlang, AFAIK, has this as its universal “all ecosystem libraries are built this way” standard. If you want this kind of fault-tolerance from random libraries in other languages, you tend to have to wrap them yourself to achieve it.
(You could say that things like independent COM apartments or CLR application domains which load into a single process are similar to this, but those approaches bring with them the overhead of serialization, cross-domain IPC security policy enforcement, etc., making them closer to the approach of just building your program as a network of small daemon processes with numerous OS IPC connections. Erlang is the “in the small, for cheap” equivalent to these, for when everything is part of the same application and nothing needs to be security-sandboxed from anything else, merely fault-isolated.)