Anyway, a sane GM would use a different difficulty scale for research than for basic knowledge.
PS: The Internet is a Mediocore (+0) library if I remember correctly.
I'd agree with this statement. The difficulty of a research roll should be equal to how hard it is to find the information. Given the ubiquity of access to the Internet then the difficulty of finding things capable of being found on the internet is mediocre (+0).
Equally, using Lore to identify things on the spot without research is going to be more difficult then when doing so in the safety of your library. For example, remembering what sort of supernatural creature eviscerates a person and alternates between a male victim one night and a female victim the next is likely to be a Superb (+5) difficulty Lore roll. Doing so in your Library with access to all your books makes it easier, and thus only requires a Good (+3) difficulty Lore roll.
Take for example, a character, hereafter called Jack, with a Great (+4) Lore and a Superb (+5) Resources which gives a Good (+3) Library. If Jack tries to identify our eviscerating demon, above, in the field (difficulty +5) he requires a +1 or better result on his dice roll. He has to drag through his memories of what he’s read etc., and identify which eviscerating demon it is. If he can take the time to research it properly in his good (+3) library, however, the difficulty roll is only +3, and he succeeds on roll of -1 (Great (+4) Lore) or better.
The Library limits the difficulty of the question you can answer. The difficulty of a question should be related to where you are, time constraints etc. A good (+3) library is therefore useful even to a character with a higher Lore skill.
Another thing to remember is Lore covers more than just research. For example Jack has a Lore of Great (+4) for Thaumaturgy but is limited to his good (+3) library for the difficulty of research questions.
I would also agree that you could purchase a Stunt to improve the rating of your Library.