The simple answer
It's hysteria and plain stupidity, not based on any objective facts, but you cannot do anything against it. The airline follows a recommendation by the FAA, and whatever the FAA says is pretty much "The One And Only Truth" (well, not exactly, but... it's what applies, anyway).
They tell you "phone off", and you had better comply, or it may get very expensive and uncomfortable for you.
It is highly likely that other airlines (with few, if any exceptions) will follow this example, if for no other reason than because they want to eliminate every possibility of a liability.
A more elaborate answer
All batteries (or more general, all energy carriers, and energy converters) are dangerous. This is a necessary consequence from storing and converting energy.
Batteries, and in particular lithium ion batteries (which can store a lot of energy compared to their weight) have gained particular media attendance ever since becoming mainstream. Used to be cell phones were banned from gas stations because of the risk of explosions. I'm not aware of a single case where conclusive, unalleged evidence was presented that a cell phone caused a fire at a gas station.
For fairness, it should also be noted that battery fires (not just in phones, but also e.g. electric cars) generally do not occur during normal operation when a device is turned on. In theory, this is of course possible, however, it just isn't what happens in practice.
Catastrophic things happen, if they happen, when the battery is being charged (especially turbo-charged, or turbo-over-charged), or when you do things that you really shouldn't be doing to a battery, such as crashing a car into it at 180km/h (happened in China last year), pouring gasoline over it and lighting it, driving a nail right through the battery, or deliberately provoking a short circuit with a piece of wire. Or, other things that are outright nuts.
The detail about charging is the only one that can reasonably happen in normal operation if you are unlucky to have a somewhat crappy battery (thanks to everything having to be super cheap nowadays). But even so, it is not much a surprise. Indeed, it is a perfectly normal thing for a battery to considerably heat up during charging, especially towards the end of the charge cycle. Only just... it preferrably shouldn't catch fire!
What's to be learned from this? Well, don't charge your phone over night, and don't hit it with a hammer, and you will be good until you get a replacement. The idea of preventing incidents by not turning on devices is... funny. But, unluckily, in this case it's not reason that counts, but what you're being told.
That aside, there is an accepted standard for representing defects of any kind in the industry (... any defect, any kind of industry), the famous six-sigma, or 3.4 DPMO ("defects per million opportunities") figure. Note that a "defect" can be anything from a customer being unhappy with phone support being unresponsive, or simply one guy in the company not getting his report in time, to a piece of clothes having a bad suture, or, well... an airplane exploding mid-air. There exists an entire specialist industry around applying this principle.
It is universally accepted that reaching "six sigma" is the holy grail. In practice, few not-life-threatening products or services even come close (most are more like 3-4 sigma). The reason is simple: It is exceedingly difficult and expensive to have such a low defect rate.
It so happens, however, that 3.4 DPMO (6σ) is universally considered the gold standard for battery safety. Which means you must meet this target to avoid people pointing fingers at you.
Now... the particular model manufactured by Samsung had 35 defects with catastrophic failure in 2 million units sold. That is 17.5 DPMO, or 5.7 sigma. Not bad, but clearly, Samsung has failed to meet the standard. But what does it really mean? Are all Samsung phone owners going to die in a fiery inferno?
Tesla had 2 battery-fire incidents (that made it to public!) among 100,000 units of Model S produced. That's 20 DPMO, worse than Samsung's. Did the Department of Transports ban Tesla cars from the streets?
Boeing, a leading airplane manufacturer, had 4 confirmed lithium-ion battery fires (that made it to public!) among 455 produced units of its 787 model. That's 8,790 DPMO, and you would be inclined to think that an airplane is a somewhat more "mission critical" thing than a cellphone. Should we ban Boeing airplanes?
Nokia and Sony had similar events like Samsung in 2004 and 2006, but on a much larger scale (Sony was around 10 million units, and that was when the mobile device market was about 1/5 of what it is now!). Only just they didn't make a big fuss about it like Samsung did. BYD had several incidents that were played down. In some, people burned in their cars. Fujitsu, Sharp, and IBM, they all had at least one fire-hazard battery recall in the 6-digit scale during the last 10 years. At the present time, HP is running a battery recall/replacement program due to fire hazard for the ProBook and Envy, Presario, and Pavillon lines sold between 2013 and 2015. Only just, it's not big news all over the media.
You have your company's server in a datacenter that guarantees 99.9% uptime? Well, congrats, that is 1,000 DPMO. If you can guarantee zero failures that are within your responsibility, your business still only operates at a sigma level of 4.5.
With these numbers in mind, I think Samsung did a good, responsible move at risk mitigation (in face of a not truly critical failure rate), but a truly terrible job at Marketing.
The result is, well, the hysteria that you see.
(No, I don't work for Samsung, and I don't own Samsung stocks. I don't have a Samsung phone either.)