They're only taking money from accounts that are larger than the government insures, correct?

e.g. The FDIC in the US insures accounts up to $250,000, so they would be taking money that is beyond that $250,000? In this case, it's 100,000 euros?

Just want to make sure I'm getting this right. If I am, then the people losing money are fucking idiots.

Why would you ever have uninsured money? Just split it between accounts??