So, in my symbol of Zuggtmoy example, assuming that the response to, "Is that symbol something [my character] might recognize?" (ignoring the dice roll for the time being) was something along the lines of, "what part of [your character's] background might have given him previous exposure to that symbol?" How closely does the player's response (given that the player may or may not have any idea what the symbol might be representative of) need to match the context of the symbol? Also, how much sense does it need to make?
Would, "[my character] spent four years studying symbols and their meanings." do it? What if the character was a barbarian? How about, "[my character] took two semesters of symbology in community college" Would it matter that the possible presence of community colleges, while not typically part of the genre, had not been explicitly ruled out? How about, "As a sailor, [my character] spends a lot of time in tattoo parlors?" What if that same sentence started with, "As an accountant"?
If the character had previously been described as being knowledgeable about religious symbols, but due to lack of context said instead, "[my character] has spent some time tracing the activities of the local slavers." Would you still give them the information on Zuggtmoy? Would you deny them any information at all? Would you tell them that the symbol had a religious significance, but that they couldn't bring it to mind?
What if the player used the same (seemingly reasonable) rationalization every time, "[my character] spent twelve years apprenticed to a wizard that made him recite lines from obscure tomes on demand."
These are (to me) practical, rather than rhetorical questions, as I may want to try something like this. So, while some of the questions seem somewhat nonsensical, take that as an indication of the type of play I expect from my group.
It's a case-by-case thing and hard to judge without the full context of the knowledge of the characters who are adventuring and the established obscurity of the knowledge itself. As long as the player is making a declaration in good faith, I tend to err on the side of the player and at least ask for a check. If the player's declaration is particularly relevant, then I'll just grant automatic success. It's fairly rare that I'll just say no, but I will when it makes sense. And players in general self-select on this sort of thing in my experience, judging for themselves whether their character might know about such things or not. I wouldn't see five players all trying to justify knowing that symbol in practice, for example.
In the example of Quiet Riot's tattoo that I mentioned upthread to [MENTION=6777696]redrick[/MENTION], two of the five players chimed in to try to identify it. Carl Lagerbelly, the paladin, drew upon his religious training. I didn't think that was appropriate, so I said that it was beyond the scope of what the church taught him - fail, no roll. Robert Bob Roberts' declaration seemed more reasonable, if a bit of a stretch given the context, so I called for a DC 20 roll which he exceeded.
There's also the issue of the meaningful consequence of failure. In a simple binary transaction, you recall it or you don't, so it would have to be a situation where not recalling it has some kind of consequence associated with it. If it doesn't, then the DM can just say they do or do not recall the relevant info. In the case of Quiet Riot's tattoo, that cost might have been being fairly blindsided (potentially) when it is revealed she's a bit shadier than they might otherwise expect. Fair enough for a roll, I think, in this situation.