Indeed. Wasn't this exactly was Greece was already doing with half of the population?
No it wasn't. Greece's public sector is at 22%. Which is not small, but it is not the thing that got the country into trouble. Even the UK has more public sector employees let alone the northern european countries like Denmark and Norway that go up to 35%.  Anyway, the word universal on UBI does not mean "half the population" nor 22% of them, and that distinction is quite important.
Greece's main issues where the same issues that most countries face, only a bit bigger. Corruption was rampaging. The local (and european) elite were bathing themselves with public money. They owned the media and the governement for the last 20 years. The public insurance institutions' assets have been handed away again and again on pyramid schemes like the stockmarket bubble in the late 90's (Greece's stockmarket soared to 7000, only to return to 1000 a few months later). Public money were been wasted on a huge military budget as a result of under the table agreements between Greece and the US, Germany, France and sometimes Russia. At some point they even legitimized corruption and getting a cut for every agreement. Sure, there are many issues on public spending and efficiency that should've been improved, but that was only a small part of the problem.
Claiming that Greece has a UBI of a sorts is not backed up with data unfortunately. Greece has had issues with income inequality before the crisis struck, but with the austerity measures and the economy taking a dive, this has only gotten worse 
The problem with taxing the rich folks is not that they will move their money away. They are already doing that. You can not compete with tax havens. But what is evident from the recent Panama leak (and the swiss and Lux before it) is that governments are not only unwilling to tax them, but they are part of the scheme. You can not honestly believe that the US can not force Panama, the UK the Cayman or the EU Luxembourg to play nice and hand over the data.