I don't think the examiner is intentionally distinguishing between bound or free electrons (this is probably just sloppy language). The scattering is just proportional to the number of electrons that are there --- more precisely the structure factor (whose square is the scattering amplitude) is the fourier transform of the electron density rho(x)
The thing the examiner was upset about is that no one noticed that this is Thompson scattering -- effectively the same as photons scattering from free electrons. The point being that the electrons can be considered free because their binding energy is so small compared to the energy of the photon.
The fact that the scattering is proportional to the electron density is certainly a result of Thompson scattering -- but should also be obvious. If there are twice as many electrons to scatter from you should expect twice the scattering amplitude!
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