Does Fibre Optic Cabling have any potential for noise?

You are right, this is the case but fiber optics can still have problems that can be perceived as noise that lead to incorrect data:

Intersymbol interference: This is a kind of noise because the previous symbol that was sent will interfere with the actual symbol that is being sent. Thus the previous symbol will act as noise. Well known techniques to help it are called Orthogonal frequency-division multiplexing (OFDM) and Orthogonal Frequency Division Multiple Access (OFDMA). You can find whole books about intersymbol interference.

Chromatic dispersion [ps/(nm·km)]: The refractive index of fibers varies slightly with the frequency of light, and light sources are not perfectly monochromatic. This has the effect that, over long distances and at high modulation speeds, the different frequencies of light can take different times to arrive at the receiver, ultimately making the signal impossible to discern, and requiring extra repeaters or special cables with adjusted indexes for every wavelength (so they arrive at the same time).

To make proper comparisons between fibre and cable you have to consider the photodiode at the end of the fibre to be part of the fibre and this is the weak link in terms of noise. Typically the Hamamatsu S5973 photodiode produces a noise equivalent power (NEP) of \$1.5 \times 10^{-15}\$ watts per Hz and given that the device is good for 1 GHz the noise power is going to be about 1.5 uW.

This photodiode converts watts to amps at approximately 2:1 therefore the noise current is about 0.75 uA RMS. You then have to ask yourself how much "signal" current is the photodiode producing and how this compares to the noise current.

I'm just trying to point out that you need to compare apples with apples.