If you are the pilot in a situation like this, does the airline say, "Alice, you did good. Take the next month to yourself." Or is it just business as usual, "See you on Monday." kind of deal?
Your wife asked you for a divorce last night and you can't focus on work? You can call out without consequences.
You just couldn't sleep and don't feel able to fly? Call out.
They understand the importance of the human factor here and would much rather have to reschedule a flight than have a potentially impaired person make a mistake.
Obviously if you're doing this regularly, you're going to have a conversation with management or the chief pilot or someone (I've no idea what the actual reporting structure is) but if you don't abuse the policy, you can call out without consequence.
I don't know specifically about FedEx but I imagine they have something somewhat similar, the FedEx/UPS pilot jobs are also considered top tier (but not nearly as top tier as a major long-haul position) with good benefits.
I do imagine, especially considering how much press this is getting, that the pilots in this case are going to spend the next week or two doing paperwork and maybe some press even. How quickly they return to flight will probably be dictated primarily by how they feel. Fact is as dramatic as this seems to us it's possible the pilots are completely unfazed and just want to get back to work. I think if they wanted a week or three off to recoup that FedEx would make accommodations. Pilots seem to be treated reasonably well at major airlines (ignoring regionals and subsidiaries, where they are cattle) and the possible negative value of negative press (FedEx fires pilot who saved plane from near-miss for asking for time off to recover!) this should be a no-brainer for them.
Pilots also have a good union behind them.
Pilots and airlines do not seem to shift fault away from themselves but seem to do a phenomenal job of identifying root causes to avoid future incidents.
The Wikipedia info box summary is "Runway overrun caused by pilot error". And indeed, the pilots were going too fast with the flaps set wrong. At some point, they indeed faced a difficult decision, but one that was caused by their own, multiple previous errors. Having made that decision incorrectly, they also failed to stop the aircraft as well as they could. From your link:
> In the end, the NTSB identified two separate decisions by the captain which led to the accident: first, his decision not to go around immediately when the plane started to float, which was inconsistent with his training; and second, his decision to finally go around after it was already too late to do so. The float itself was caused by excessive airspeed on touchdown, in combination with an ill-timed gust of wind. In a later revision suggested by the Air Line Pilots Association, the NTSB also added the “non-availability of information about the aircraft’s go-around performance capabilities” as a contributing factor to the captain’s decision.
37 people died and the pilots kept their jobs. Truly amazing job security, much like this other example where the pilots almost killed 1000 people (but didn't in fact kill any): https://news.ycombinator.com/item?id=34395221
When you see the regular incidents that do not result in crash, that statement would be obviously regarded as false. Yes, things are mostly reliable because most of the time there are at least several safety features or processes in the way, but most crashes and incidents are still due to human error.