Whenever I hear about someone selling at a loss, I automatically assume that either they’re buying market share as a long bet (e.g. typical new gaming console) or more commonly misrepresenting the actual economics (e.g. car dealers neglecting to mention all the rebates they get off their supposed price).
You're basically betting that the other guy doesn't have the stamina to survive at this price.
Of course, if what the OP says is true, if the other seller has a much lower price point than you do, you can't outlast them. They could still be making a profit at $20 while you're losing $5 per unit trying to push them out.
And to your car dealership point - the way it works for GM at least is that GM sets sales goals for their dealers. Dealer X's monthly sales target is 75 vehicles. They will happily sell lets say vehicles 73, 74, and 75 on August 31st to get their $20k bonus for the month of August. They might not be misrepresenting their supposed price like you think. Also, the same concept of inventory holding costs applies really well for car dealers. It's purely an inventory turnover business. If your lot is full of fusions and you can sell 2 f150s in the time that you can sell 1 fusion at similar profit, you're going to want to get those fusions off the lot potentially at a loss so you can sell more f150s.
In my particular case, there is an "anti-FBA" culture at the company I work for. No one can sell our product for as cheap as we can because we make it. However, without access to FBA, it's much more difficult to have complete control over your pricing on amazon. With complete control over pricing you can ensure that your margins will be better than whatever distributor pricing is. Also the competitiveness of our products on the platform against other brands is directly affected by how much the seller (either us or an unauth)can afford to sell the product to the consumer. If a competing brand sells the same thing for cheaper, they will get more sales and thus more market share.
I say "my particular case" but in reality I know of several CPG companies where the anti-FBA culture exists, even though it is the most advantageous approach to selling on amazon with regards to pricing. I wrote this kind of fast so I hope it all makes sense.
Did you notify Amazon or any authorities about this? Would be curious to hear the response.