Forget about getting brown from green and red, I can't for the life of me think why people keep telling you that green and red make brown, green isn't a primary colour, it is mixed using yellow and blue, your problems begin when the green you use was mixed out a yellow or blue that wasn't a primary because you won't get brown you seek and adding anything else to them will make them behave unexpectedly, not mention that you would be restricted to the percentage of drops of each used to produce the green in the first place, by using proper primaries of red, yellow and blue you have total control over what happens once you get the hang of it, if you mix say canary yellow, crimson red and air force blue you would end up with with something resembling mud.
The reason you were able to get a brown by adding orange to black, bearing in mind orange is red and yellow, is because in airbrush paints the black is made up of the colours used in printer inks, i.e. Cyan, Magenta and yellow, Cyan is very overpowering in the mix but when you mix all three you end up with black instead of brown as with the true primaries, this is why your colour printer inks diminish even when you print in black and white, your printer uses both your black cartridge and your colour ones, the fact that the blue is overpowering is also the reason we get the dreaded blue shift when we go over black with white, but as I mentioned, the addition of orange, or as I like to call it, yellow and red counteracts this unwanted event because the the blue consequently becomes less overpowering.
Here's is a little trick for you to try out just for fun, the colour wheel you showed above, print out a copy of it, attach it to a drill or an electric eraser and let it spin, doesn't need to be really fast, if you try to look at the colours while it spins you will see only white