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I was going to ask the same thing -- maybe someone more astronomically inclined has an answer to this...

If one were to take a phot of our solar system, would our asteroid belt really be dense enough to show up in any wavelengths?

The most likely explanation to me is that the author is just wrong in describing it that way and it's a much more massive debris disc slash protoplanetary disc.

Maybe because it's still gas and dust, whereas if the same mass coalesces into large objects it's much less reflective?

At a guess - very long exposure times. Even if it's only sending one photon per second in our direction, if we stare at it long enough then eventually we'll have an image.