When consideruing classical FRW I was talking about classical GR; it shows that even classical "flat spacetime + small oscillations" does not work for all classes of solutions of GR. It's the same with strings: they find a huge number of classes of "classical solutions" and consider small oscillations for each class. The big difference is that for different "classical solutions" one has to consider different oscillations, i.e. the particle content is different.
It's hard to compare ST and LQG here.
ST always uses these "classical solutions" and constructs a quantum theory on top of them. So for each class you get a quantum theory, but in a sense you don't have the big picture, i.e. no unique quantum theory (string theory) describing all these classes at once.
In LQG it's exactly the other way round. They claim to have a unique quantum theory of gravity (w/o particle physics) w/o the need to introduce these classes. But at the samepoint this is the weak point of LQG b/c they are not able to derive the classical solutions, i.e. they don't have a way to extract the classical physics with different spacetimes we know from GR (there are only very restricted models or methods from which they get rather specific spacetimes).