On my R1200R, which I've ran out of fuel numerous times on, I never could get more than 5.2 gallons in the tank. That's filling it completely to the top when the recommended way to do it is only to fill it to the bottom of the orange filler neck.
I've not ran out of fuel yet on the ninet but assume it will be the same way. There's .4 gallons of space left at the top of the tank to avoid spilling fuel out is my guess.
That's on the R1200R though, but I don't see BMW changing things like that. If the bike had a 5.6 gallon tank, they would certainly market it. It could be just a bad translation if that's what the manual says, that wouldn't be the first time.
My light is coming on pretty regularly around 170 miles now that I have some miles on the bike, 42 mpg on average, exactly the same as my 12R.
120 miles seems a bit low for the light to come on but I don't know how many miles on the motor or how hard you're riding. I think early on during break-in maybe my light came on once at 135 miles.
4.8 gallons is the total amount of the tank capacity as listed with the recommended way of filling it. I don't think there's a .8 reserve and if the fuel strip is accurate it will turn on the light after you burn about 4 gallons.
If someone runs the tank dry, please let me know if my guess is correct or not.