Interesting question. My thoughts on this are that obscuring information is helpful to security in many cases as it can force an attacker to generate more "noise" which can be detected.
Where obscurity is a "bad thing" can be where the defender is relying on that obscurity as a critical control, and without that obscurity, the control fails.
So in addition to the one you gave above. An effective use of obscurity could be removing software name and version information from Internet facing services. The advantages of this are
- If an attacker wants to find out if a vulnerable version of the service is in use they will have to make multiple queries (eg, looking for default files, or perhaps testing timing responses to some queries). This traffic is more likely to show up in IDS logs than a single request which returned the version. Additionally fingerprinting protocols aren't well developed for all services, so it could actually slow the attacker down considerably
- The other benefit is that the version number will not be indexed by services like Shodan. this can be relevant where an automated attack is carried out for all instances of a particular version of a service (eg, where a 0-day has been discovered for that version). Hiding this from the banner, may actually prevent a given instance of the service from falling prey to that attack.
that said, it shouldn't ever be the only line of defence. In the above example the service should still be hardened and patched to help maintain it's security
Where I think that obscurity fails is where it's relied on. things like hard-coded passwords that aren't changed, obfuscating secrets with "home grown encryption" or basing a risk decision on whether to patch a service on the idea that no-one will attack it. So the kinda of idea that no-one will find/know/attack this generally fails, possibly because the defenders are limiting their concept of who a valid attacker might be. It's all very well saying that an unmotivated external attacker may not take the time to unravel an obscure control, but if the attacker turns out to be a disgruntled ex-employee, that hard-coded password could cause some serious problems.