“Legitimate” in this case refers to any miner who is mining honestly and is simply motivated by profits from the block reward and fees. If we ignore potential price increases and inefficiencies, an ideal mining market should see block production costs increase until the profit margin for such miners is close to zero. But miners with “ulterior motives” can extract more benefit from mining, and so can mine profitably even when production costs are very close to rewards. This means in theory such parties are likely to dominate the mining network.

“Ulterior motives” includes a lot of things. It definitely includes money laundering (see Iran and China) but it also includes people who mine so they can conduct 51% and MEV attacks on the network. On the positive side it may include pseudo-altruistic types such as major currency holders, who are willing to mine at a loss in order to support the currency’s value. The thing all of these parties have in common is that none of them are incentivized to mine honestly solely because of the intrinsic profits involved in mining: your hope is that their ulterior motive is compatible with honest behavior. When that isn’t born out, your network runs into trouble.

* Obviously in the real world there are tons of capital expenses and prices fluctuate wildly, so this model is loaded with inefficiency that can allow some folks to make money on mining as a business in and of itself. But PoS systems will have fewer such inefficiencies.