that's part of their fallacy indeed. they use "cost" to refer to things that encompass their and other prices, but prices don't have to do with cost. in competitive markets, price tends to cost, but in distorted markets, such as those one enters when adopting nonfree software, it is arbitrary monopoly pricing. this affects the price of the entrance ticket as well. markets that are distorted by such power dynamics can offer lower entry prices, to bait naïve customers and get them hooked (locked in), so that they're forced to pay more later. in some cases this sort of price distortion is called dumping, and it's outrageously illegal. in other cases, legislators overlook it, even when it comes to spending of public money.
so, no, nonfree software doesn't always get a lower cost (price, really) when they torture the numbers so that they tell the story they wish the to tell, cutting off the time range before the locked-in customer has to pay back or pay to leave, or when there's dumping in disguise. it doesn't get a lower cost either when only a few are paying for the development and maintenance and support, instead of dividing that cost among gazillions of users forced to buy the product whether or not they want it. but yeah, overall, if you do the maths right, free software must always cost less in aggregate.