That is definitely not right! I did my floors myself and managed to get the marks out! He has missed out on the grits somewhere. Isn't there an industry standards body to talk to?

No, those marks should not be visible. It looks to me like they are caused by screening and the stain highlights any marking in the surface

I get really irritated when people have problems with the floor surface and go ahead and apply the finish coats without having the customer OK the stain color and surface. That problem could have been much more easily remedied before the finish was applied

In my opinion, his comment is covering up lazy workmanship. Not only is this a grit issue, the machine hasn't been pushed smoothly over the floor. There is no reason to have "half-moons" over the surface.

I have hired many contractors and this is unacceptable workmanship! Don't pay and take plenty of photos. Does he have insurance and what about the contract?

I don't believe this is an issue involving either skipping sanding grits or uneven machine feeding. The key clue is the circular nature of the marks...drum sanding issues leave linear marks. Uneven sanding tends to give an "ocean wave" appearance. Small circular swirls around the perimeter are from an edger while larger arcs in the center of the room come from problems with the screening done after sanding.

I also don't image this is lazy either...you would have had a better result if he had skipped the screening step altogether and simply waited until after the first finish coat to screen the floor (recommended procedure when using a dark colored stain). Lack of knowledge perhaps or poor workmanship would be my opinion. I'm just mentioning this as it might help you decide what approach you wish to take when deciding how to deal with the remaining payment for the work.

At this point in the process, it isn't a problem which can be easily fixed. It isn't a glaring issue so I would not resand the floor to get rid of these marks. The marks won't be all that noticeable when you get rugs and furniture in the rooms.
Just curious, how does the floor finish feel? Is the surface smooth as silk or does it have a gritty feel? If you look at it from a low angle with the light shining across the surface, does the surface appear even?