Corruption, that's why. Similar to how the Italian mafia would half-build highway bridges with taxpayer money and then mysteriously have some shell company go bankrupt. OLAF is on it because of course they are when stuff makes the press. If they have a case EPPO will take over at which point that Hungarian mayor will have the questionable honour of being up against the gal who cleaned up Romania... before Hungarian courts. If those turn out to be corrupt then that's going to buy the mayor time but ultimately the ECJ would overrule them. Still no mechanism to actually set boots on member state grounds but Hungary is already on thin ice when it comes to getting suspended from the EU for various reasons, they're going to tread lightly.
See if you want to be corrupt in the EU you have to do it like the big boys: Implement some policy, then get a cushy job at a company. Or receive tons of money for boring private speeches. Something like that, directly grabbing into state coffers is so uncivilised.
EDIT: Oh, Hungary didn't join EPPO, figures. They can still freeze assets, though. Also if I understand things correctly our mayor would turn into a fugitive in the rest of the EU.