I found the answers a bit confusing so let me say it another way. The noise source is the resistance of the switch. When the resistance is put in series with the cap the whole thing acts like a low-pass filter with a cut-off of 1/(2*pi*R*C) since you are taking the voltage across the capacitor. The resistance value falls out of the equation when you sum up the noise over the entire frequency band.
The reason it falls out of the equation is that a larger resistance will generate more noise, but the capacitor interacts with the larger resistance, rolling off the noise at a proportionately lower frequency. So a large resistance will generate a lot of noise, but the bandwidth will be small. Conversely, a small resistance will generate less noise, but the bandwidth will be proportionately larger. Either way, the total noise stays the same.
A derivation of the result is
here and in most decent textbooks.
Note that this is just the noise put onto the capacitance by the switch. The amplifier also adds noise. Also, a larger switch resistance filters off the noise from the voltage you are attempting to sample, so kT/C is a bit of a lower limit on the total noise.
rg