Actually I think the idea of the holographic principle is that, as in a holograph, all the information in the 'bulk' is already present at the 'boundary'. So, it claims that any calculation involving bulk observables can be expressed in terms of boundary observables. It may not claim the reverse, though that could often be taken for granted!
In discussions with Urs Schreiber and Jamie Vicary we seem to have settled on the following formulation. A modular tensor category gives rise to a once extended 3d TQFT and can also be reconstructed from this once extended 3d TQFT. By work of Fuchs, Runkel and Schweigert, a modular tensor category equipped with an equivalence to a category of representations of a vertex operator algebra and equipped with a symmetric Frobenius object gives rise to a rational CFT.
The italicized phrases would then be ways that the rational CFT has more information than the once extended 3d TQFT. The first one gives the 'local information' needed to construct a CFT locally starting from the extended TQFT. The second one gives the 'global information' or 'sewing information' needed to finish the job.
Apparently there may be one, many or no rational CFTs corresponding to a given once extended 3d TQFT.