Fluorescence resonance energy transfer (FRET) measurements allow one to observe site exposure in nucleosomes, i.e. the transient unwrapping of a part of the wrapped DNA from the histone octamer. In such experiments one can typically distinguish between a closed state and an open state but in principle one might hope to detect several states, each corresponding to a certain number of open binding sites. Here we show that even in an ideal FRET setup it would be hard to detect unwrapping states with intermediate levels of FRET efficiencies. As the unwrapped DNA molecule, modelled here as a wormlike chain, has a finite stiffness, shape fluctuations smear out FRET signals completely from such intermediate states.