Yes, quite correct when using a 720nm pass filter you will have visible light leakage which can be manipulated in PS by channel swapping red for blue, and of course all the other "toys" PS offers. The deeper you go into NIR, such as 850nm or even the Hoya 1000nm, you lose any visible light and the images do become more monochromatic.
What prompted me to get the camera was an interesting meeting with a Fuji rep at last years' photoshop world convention in Las Vegas. He was a forensic photographer by trade and showed me some portrait work (on live people, thank you) he had done. The skin tones were amazing! I was telling him about the type of photography I like to do (marine environments) which led to a lengthy lecture on the benefits of NIR shooting in hazy conditions. Then he said the magic words. He could get me one at factory cost.
I'm sadly the kind of person who will jump at almost anything offered at "factory cost"... need to get rid of 1000 lbs of lard? Factory cost, baby! I'm your man!
So that's the back story. I'm just learning this type of photography and am the first to say that the results are perhaps an acquired taste. But it is fun, different and I know the shutter will wear out long before my NIR learning is complete.
Digital infrared is 'near infrared' was my understanding, so that some false color is maintained in the channels which can be enhanced through normal Photoshop adjustments.