This is the thing the contractor quoting you $8,000 will not say out loud, because it is not in his interest to say it.
White scratches on hardwood floors are not gouges in the wood. They are grooves in the finish that have filled with air.
Air catches light differently than the finish around it. That is why the scratches look white. The same reason snow looks white. Snow is not white. It is clear ice with air bubbles.
The wood underneath is almost certainly fine. Oak is hard. You would have to work at it to actually damage oak.
Anyone who looks at your floor sees white. What they assume when they see white is damage. What they do when they assume damage is either mentally write off the floor, or start calculating what it would cost to fix.
The gap between what the floor actually is and what it looks like is the whole problem. The fix is not refinishing. The fix is filling the air.