As a pilot, there is always another party that could put in paperwork...
As an ATC we supposedly have a 'no fault' culture. If you put your hand up you are likely to get some sort of managerial support, for whatever that is worth. If you don't put your hand up you are very unlikely to receive any support except from your union and even then they might cut you loose when it comes out, because more than likely it will...
More than likely the pilots would have noticed an ATC breakdown especially since TCAS now has a wider audience; although sometimes this won't always be apparent to pilots... But an airprox certainly would be.