Help understanding current noise
Ah, good-old front page data sheet claims and misunderstandings and, I think TI are one of the worst for the stuff they put on their front pages but, on this occasion they are not lying. Firstly what they say: -


  Because of the ultra-low input current noise of 0.13 fA/√Hz, the LMC6001 can
  provide almost noiseless amplification of high resistance signal
  sources.  Adding only 1 dB at 100 kΩ, 0.1 dB at 1 MΩ and 0.01 
  dB or less from 10 MΩ to 2,000 MΩ, the LMC6001 is an almost noiseless
  amplifier.


This has nothing to do with the the current noise; after all it is very very small and is discountable. The big curse of this device is the equivalent input voltage noise of 22 nV / √Hz and it is likely that this is what they are referring to in comparison.

Also they are really talking about noise-figure and I'd refer you to the graph on page 12: -



So, as the graph predicts if the source impedance is 100 kohm the noise figure is 1 dB; falling to 0.1 dB at a source impedance of 1 Mohm and 0.01 dB at a source impedance of 10 Mohm.

They are comparing the effect of the 22 nV/√Hz (probably over a bandwidth of 1 kHz) with the much bigger noise due to the source impedance. So, over a 1 kHz bandwidth, 22 nV / √Hz yields a real RMS noise of 0.695 uV but, the source impedance produces a noise of 1.27 uV RMS when it is 100 kohm. At 1 Mohm the source impedance thermal noise rises to 4.023 uV and this noise is 10 dB higher than when the source impedance is 100 kohm.

Hence the noise figure is 10 dB improved. "What" you might say? Noise figure can be confusing and I suggest you get the definition from Wikipedia: -


  The noise figure is the difference in decibels (dB) between the noise
  output of the actual receiver to the noise output of an “ideal”
  receiver with the same overall gain and bandwidth when the receivers
  are connected to matched sources at the standard noise temperature T0
  (usually 290 K).


And what this means is that the noise figure improves when the input source impedance rises because it masks the inherent voltage noise voltage. Going back to the graph of noise figure, it doesn't keep on falling; it begins to rise when the source impedance is 100 Mohms and greater and this is likely due to the input current noise beginning to have an effect.