How is someone's badge security information? Anyone can walk up to the building entrance and see several people's badges on the way, surely security can't depend on keeping those secret.
By that same logic, passwords wouldn't be security information either because anyone could videotape someone typing theirs in at a coffee shop from afar. But, I suspect that's rare because it's really difficult in practice. The purpose of many security policies is to increase the amount of effort an attacker must go through.
I don't know of any company that encourages the display of passwords around their employees' necks.
well, depends if you're concerned with security or appearance of security. Security engineers need to do both.