Twilight didn 't realise how much faith he had in his daughter until she ran after Damian, and he did nothing to stop her. He agreed with Yor: that if there was anyone best placed to calm him down and explain things, it was Anya. It must have been creeping in slowly - the fact that, throughout all these years, Twilight was subconsciously training Anya, and he didn 't even know it. So when he let her run after Damian, Twilight knew that she would be able to handle the situation. He trusted her.

Who he

didn 't

trust was Yuri (for obvious reasons), and even Adrian to some extent, since Twilight didn 't know enough about him to form a proper conclusion, but that was to be expected. He would have to do his usual strategy of collecting information first.