Also I remember hearing about an anonymisation technique in which you have to trust the person who generated the first block to destroy the private key without writing it down, otherwise they have the ability to decrypt the anonymisation forever after. Is this using that technique ? If so why trust they don't have the backdoor key handy ?
Your memory is only partially right. There is a potential problem with trusted setup. They have said they play to do this in some public ceremony with multiple parties so that unless ALL of those parties collude, the minting process is safe.
If all parties colluded they could print a unlimited number of coins undetected, however the privacy of transactions would not be affected. Essentially it is an economic threat of a poorly designed setup allowing parties to collude to print unlimited coins. There is not a privacy threat from collusion.