The argument your friends advance is called “predatory pricing” in the economics literature. A firm selling a similar product with a similar cost structure as a rival undercuts a rival by charging a price below its costs. This strategy forces losses on both firms, but the predator has deep pockets and can outlast his rival. The payoff for the losses the predator suffers in displacing his rival come if and only if he is able to recoup his losses (and more) by earning excessive profits in the absence of the competition of his rival. Obviously, for this strategy to work, it must be nearly impossible for a rival to arise in the wake of the excessive profits earned by the predator. The classic article showing how difficult this is to achieve is by John McGee. Here is a short article on the topic:
Predatory pricing cannot be done by a retail firm. If Amazon drove Diapers.com out of business by undercutting both of their costs (in particular, paying the wholesale price to buy diapers from say Pampers), then as soon as Amazon raised its retail price after pushing Diapers.com out it would also be profitable for another competitor to step in or even for Pampers to sell online.
Tom DiLorenzo has written extensively about antitrust, monopoly, and competition:
Here is Dom Armentano’s book, Antitrust the Case for Repeal: