"Number of fields" is not a well-defined concept1. Here are some reasons that come to mind:
One can always introduce extra "auxiliary" fields, which can be integrated in/out, changing the number of fields.
Given two fields $A,B$, one can always define a tuple $\vec C=(A,B)$, which now counts as "one field", or does it? Conversely, does a vector field $A_\mu$ count as one field, or four? It seems reasonable to count fields as irreducible representations, but representation of what group? Only Lorentz? or also flavour symmetries? One could even introduce a "master" group under which all the fields transform together, as the components of a single field in the fundamental representation2.
Some systems have different descriptions (also known as dualities), where each description has different fields (and perhaps even different worldsheet dimension, as in AdS/CFT-type situations). So even the "field content" of a theory is not an intrinsic concept: it depends on the frame of reference, so to speak.
Etc. The claim "In String Theory there is only one master field" is meaningless. It is neither true nor false.
That being said, the standard presentation of String Theory contains 26 worldsheet scalars in the bosonic string, and 10 scalars plus 10 fermions in the supersymmetric case. Plus ghosts, if you want to count those. If you do not want to count ghosts, then it seems reasonable to gather the 26 scalars into a single vector (which is irreducible with respect to spacetime symmetry, namely the Lorentz group), and the 10 boson/fermion pairs into a single Wess-Zumino multiplet (which is also irreducible with respect to spacetime supersymmetry). So it is not unreasonable to claim that there is a single field, but again: this is so if you ignore ghosts, and think of the target manifold as that with the relevant symmetry group. With respect to the wordsheet, the fields are independent, and it is perhaps more natural to count them separately. An in the infrared the natural degrees of freedom are those of supergravity, which has a completely different field content.
1: This is why c-type functions, à la Zamolodchikov, are so useful: they give you an unambiguous definition of "number of degrees of freedom". In String Theory the fields are, in a sense, free bosons and free fermions in two dimensions. Roughly speaking, for free fields one has "central charge = number of fields", and so the latter is better defined than in typical QFTs. But this is a gauge theory, so it is still somewhat subtle. Anyway.
2: Needless to say, this "master" group is not a symmetry, but being a symmetry is a subtle concept, e.g. some groups that may appear to be actual symmetries are violated by quantum effects, and vice-versa.