The bastion host is not strictly necessary in the process. Although mfdutra didn't spell it out explicitly, they clearly have a means for accessing their core servers without needing to get on to the bastion - that's where the signing by hand comes in. The benefits of using LDAP in that case justify the cost of having an external dependency - by integrating with the central password store, the bastion provides a path into the system that delivers the desired security features (centralised identity management, auditing back to individual user accounts), but other paths can exist if needed.
That trade-off isn't applicable to core servers. If they use LDAP (exclusively) for authentication and the directory is down then you're hosed. There's no other path into the server that you're trying to admin other than to get onto the server.
You could use LDAP with a fallback to some other scheme (like signed certs, or a small set of locally defined users managed with a password vault, etc) but then you've got 2 different paths onto each server and both paths needs to be maintained, tested, and regularly audited. That's certainly possible, but why would you want to when you can just have 1 authentication mechanism that has zero dependencies.