Really this depends on the texture you're using and how close to white the texture itself is. If you follow the directions someone else posted in the Grid thread:
1. Status > Unit health > Uncheck "Use class color"
2. Status > Unit Health > Color > Set to white
... and either the foreground or background (depending on your "Invert bar colors" setting) looks black, then you're using a dark texture, or your monitor settings aren't right for the lighting the room you're in. The brighter color (the background in your screenshot, and with default settings) is whatever you specified (eg. white) and the darker color is the same but the brightness is reduced to 20%.
If you want the foreground to be brighter in relation to the background, just change all the 0.2 multipliers in Indicator/Bar.lua to something else. 0.3 would be 30%, 0.5 would be 50%, and so on.
If you had made some other changes, it would probably be easiest if you just posted the changes you'd made to the old code.
GridFrame.lua line 489:
self.frame.BarBG:SetVertexColor(r * 0.2, g * 0.2, b * 0.2, 1)
that is what I used to do to get the white background. I didn't have to do anything special except alter that code and it gave me the white background.
I'm not quite sure what you're talking about with the textures. It isn't really a texture thing, just messing with the current options you can't get the background white. Same thing with the lighting in the room, not quite sure where you're going with that. I want the background white, that's it.
Only way you can in the current options is to make the unit health white and then invert it, but that will also invert the mana/power bar to a black color which I don't want.
Well at the risk of breaking everything I tried changing some lines that I had no idea what they were doing based on what was on the lua file from GridInvertedColor and what OP said he did, unexpectedly it worked. I changed the line 10 on Bar.lua inside the Indicators folder to bar.bg:SetVertexColor(1, 1, 1, 1)