Hubble detects ghostly glow surrounding our solar system

How can they possibly have enough precision in their measurements of all the other sources of light, from galaxies to dust on the ecliptic, to be confident of such a small difference from zero after subtracting them all out, when the measurements of all those light sources are affected by this thing they've claimed to find? Not saying it's impossible, but if they did it, that's a heck of a story we're not getting at all.

"Imagine walking into a room at night, turning out all the lights and closing the shades. Yet an eerie glow comes from the walls, ceiling, and floor. The faint light is barely enough to see your hands before your face, but it persists. Sounds like a scene out of a scary movie?" No, for astronomers this is the real deal. But looking for something that's close to nothing is not easy."