AAAAAAAAAARRRRRRRRRGGGGGGGGGGGGHHHHHHHHHHHH not again!!!!!!!!!!!!!!!!

BlueOne has a point about sinking lines - there is definitely an issue there - it must look natural-coloured IMHO. However I think Steve P and Birdsnest are on the money as regards floating lines. Just don't line fish - that includes when false casting - and the colour of the line will simply not be an issue. A fish should just see your fly and maybe some tippet/leader. As regards flash or whatever; I think the coating on a line will also flash in sunlight if it is shiny (as some are) and is as much of an issue than the colour. As we have heard rods can flash too. So where does it stop? Matt stripping guides and eyes, matt reels, don't wear a watch? Cam cream on arms and face? I know all these shiny things add up but good technique will eradicate pretty much all of them. I've caught as many fish with glossy rods with nickel reel seats and chrome eyes and a shiny reel as I have with a black reel and a matt black rod and a khaki line. Technique can overcome so much, and while I would not profess to be an expert fly fisherman I try my hardest to work on technique - it is the most important IMHO.
As regards what the fish sees you simply cannot say that it sees a silhouette or it sees the line colour. What it sees depends on - as Grouse says - what the fish sees and we'll never know that. However, assuming it has vision similar to ours, then what it sees depends on:
1. Angle of incidence ie angle between the fish and the line on the surface; this will either allow the fish to see the line against the background of the sky or bankside vegetation etc (whatever is above the water), or it will see the line against what appears to be a mirror in the underside of the water surface ie if the line falls outside the fish's 'window'. The reflectivity of the bottom will affect this equation too. If you don't believe me watch the Once in a Blue Moon DVD - a white line on the mirrored underside of the surface is clear to see. This is due to the line landing a little distance away and not being in the fish's window.
2. If the line is viewed against the sky or bankside ie if it is in the fish's window, then what it sees depends on the amount of natural light and the relative angle of that light expecially if direct sunlight, the reflectivity of the bottom (this all determines whether it sees a silhouette or not) and the colour of the line versus the surroundings, which cannot be a given as a khaki line may be viewed against the sky in which case it's no good at all (in theory) even though it's great if viewed against foliage (in theory). However if a fish is somewhere that nothing long and thin ever falls on the water then any colour line will spook it...
Some swear by grey lines, some by ivory, some by straw coloured, some by buckskin, some by coral, some by orange, some by chartreuse, some by green, some by brown etc etc. This goes to prove that there is simply no single answer - there are simply too many variables. I've been just as successful with a khaki line as I have with a lemon yellow one or a white one.
Pick whatever you're happy with but don't line fish, and remember that includes false casting.