still it's a sick leave; in my country a person who's in a sick leave can only leave the house in a specific schedule; there's also surprise visits from work inspectors to check if the person is not cheating the leave; if caught then they can be justifiable fired.
if they wanted to rest from stress and had no vacations left then a no pay leave is enough.
So how's the weather down there in North Korea ?
That's absolutely ridiculous. Fact is, you can be sick in many ways, and the employer don't have any rights to control what you do when you're "home" sick. while the specific rules vary from country to country and some countries have absolutely backwards rules, though not to the extent you describe(over here the work place would be charged with illegal surveillance and control measures of an employee), over here you can do whatever you want, including going away IF it doesn't negatively affect your recovery. On the same not, if you get sick on vacation, the days you are sick are counted as sick days and not vacation days. In some cases the doctros will recommend and in extreme cases even prescribe trips abroad.
But no matter what, they can't force you to stay at home, in your house. for a lot of sick reason getting out and getting fresh air is in fact something you need to do, and just because you're sick and can't be at work doesn't mean you can't be outside or such.
Being home sick and then posting pictures of yourself drunk at a party, yeah, that's grounds for a warning the first time and then firing the second time, maybe even the first time depending on the severity.
But nothing in this story indicates they broke the trust or anything of their employer. They where sick and left the country to be with friends and relax to get better. based on that video alone, this company would not be allowed under work laws to fire them.