The latter can lead to an unintended problem. I once went on an interview where I was passed from room to room, on the hour, and taken through my technical paces each time. Each interview was intensely technical. If my interview had been my only exposure to the company (i.e., I hadn't gone to the site, read press releases and articles, and so forth), I would have no idea what the company does, other than that it seems to involve operations-research style math (optimization and stochastic processes), data structures and algorithms, and complex sql. I certainly would have no idea what they planned on having me do from a business point of view. I didn't get an offer (was busy, hadn't adequately refreshed my knowledge of tree traversal, markov chains, and linear optimization to immediate post-exam undergrad/grad levels), but I wasn't hot on the company anyway, because it left me with the impression that they wouldn't value my business input in any way.
So, why would they do this? Maybe they're just sort of looking generally for people. They figure, eh, if we find candidates who can rock an exam[1], sure, let's go ahead and make an offer, I'm sure we'll find something for them to do. Because their need isn't immediate, their standards (no false positives) will be set unusually high.
The unintended consequence is that yet another developer in this space is now reluctant to interview, because who wants to prepare for and re-take their undergraduate/graduate math and CS exams?
[1] At this point, I don't even think we should call this an interview, it was an exam that lasted longer than my MS graduate exams, with far less information about what would be tested.
I think you have "false positive" and "false negative" backwards, but I agree with your point. I have long thought that the industry systematically understates the damage of false negatives and overstates the damage of false positives.
If you are hiring, it fits one of two broad categories: catch as catch can, or specific need. In a catch as catch can situation, the "always hiring" mode, the company can afford to place more emphasis on minimizing the false positive rate at the expense of the false negative rate because the desire is to skim the cream off the top of the applicant pool as it comes to you. The company doesn't need new people per se; it finds slots for these highly-capable people somewhere in the company after the hire is made.
In the specific need situation, the company is hiring to fill a hole. Either work is not getting done, or other people are overburdened with the responsibilities this new hire will take on. In this case, every day that passes costs the company in some way. The cost of a false negative is related to the quality and size of the applicant pipeline. A false negative could add anywhere from a few days, if the company has a strong pipeline, to a few months, if the company has a weak pipeline, to the timeline for filling this position. The "false negatives are cheap" position comes from the former, but I would say that very few companies actually have an applicant pipeline that strong. Furthermore, if you can go months without filling a position and not suffer any ill effects, you need to ask yourself why you are looking for someone in the first place.