[namnatulco]

"hidden" here refers to not visible to the communication partners (e.g., me and hackernews); my understanding is that government access should remain hidden to the immediate communication partners in this way. However, it should remain accountable. This is still a backdoor in the communication system by the definition you cite, although it is much less problematic than a backdoor no-one knows about (this is also what the article talks about, for example under 'vital technicalities').

Note that for the purposes the government (claims to) want access to the communication or hosts, it is _necessarily_ hidden. If it would not be hidden, that would mean a criminal(/terrorist/$insertBadGuyHere) would be aware that (s)he is being monitored, which probably does not provide the information the government (or in this case, the police or intelligence agency) is looking for.