There are hidden tori in type IIB string theory! One may describe type IIB string theory as a formally 12-dimensional theory called F-theory (due to Cumrun Vafa) whose 2 dimensions must be immediately compactified on a two-torus or, using the F-theory algebraic geometry jargon, an elliptic curve. In fact, what's important about F-theory is that it allows the $\tau$ parameter labeling the complex structure of the torus to undergo SL(2,Z) monodromies when you go around real-codimension-two objects, the 7-branes in type IIB string theory. This monodromy corresponds to the reparameterization of the periodic vectors that define the two-torus, something that is allowed at the level of (12-dimensional) geometry but something that one could forget about if he just considered a field $\tau$ in the 10-dimensional type IIB string theory.
The derivation of the S-duality group from the 12-dimensional theory is then totally analogous to the derivation from the (2,0) theory. There's only one difference: the 12-dimensional theory apparently doesn't allow us to decompactify the two toroidal dimensions: they're intrinsically different, infinitesimal dimensions. However, as far as complex structure on manifolds goes, they may be treated together with the remaining 10 spacetime dimensions.
The two-tori in the two constructions above aren't quite independent from one another. After all, an M5-brane wrapped on a 2-torus in an M-theory spacetime may be interpreted as a D4-brane in a type IIA theory (obtained by reinterpreting one of the wrapped dimensions as the 11th M-theory circular dimension) and then T-dualized to a D3-brane in type IIB string theory. The (2,0) SCFT may also be obtained by compactifying type IIB on ALE singularities which is harder to relate by dualities but I don't want to say everything about the (2,0) theory here.
M-theory (name linked to mother) has 11 dimensions and all of them may be decompactified; F-theory (name linked to father) has 12 dimensions but two of them can't be quite decompactified. Which of them has a higher number of spacetime dimensions (and is therefore a "more geometric description" of string/M-theory vacua) is therefore a bit subjective question; it's similar to the question whether mothers or fathers are more important parents. They play different enough roles in the structure of string/M-theory but both of them are comparably important.