Dark lines on pine floor after sanding and polishing, help!

We've just had the old pine floors of our 80 year old home professionally sanded and polished.

When we checked the result, our hearts sunk - there are approx 10mm dark "shadow" lines uniformly every 500mm all over the hallway and lounge room! The lines run across the grain of the floorboards. The bedrooms are unaffected.

Mr floor sander says this is from carpet shampoo and dirt seeping down between the carpet and underlay that used to cover the floors and there's nothing he can do to fix it.

Surely the floors should have been cut back to the point where any old grime that's penetrated wouldn't be visible anymore? What can we do to fix it? It really isn't a good look at all. :(

It's an 80 year old floor that shows it's history.
It was never going to look like a new floor. i've seen some pretty ugly results from a sand and polish. You can resand it until the lines disapear. You will be hoping that you dont sand through to the tongues. That will look even worse.