You are trying to set this in terms of the DM always saying "yes" or "no," when the reality is that the DM will very rarely be saying "yes" or "no." Circumstances around the PC, his skills, background, etc. will all factor into whether not the PC knows, doesn't know, or might know. For example, if the PC is from the middle of the desert and has spent his whole life there, a thousand miles from the nearest troll, it's pretty certain that he won't have knowledge of trolls based on his background. If he doesn't have some sort of skill or play experience that could give him knowledge of trolls, the DM should rule that he doesn't know about them. On the other hand, if the PC is from a town right next to the Troll Moors, it's going to be certain that he will know about them, regardless of what skills he might have. Unless there is crystal clear information like that, and it won't be that clear the vast majority of the time, the DM will call for a roll since the outcome is uncertain. Calling for a roll is not the DM saying "yes" or "no," so there is no "Mother May I possible." A few occasional instances of "yes" or "no" doesn't come close to rising to the level of "Mother May I."