I could be totally wrong (please correct me if so), but IMO there are two things happening that weren't totally discussed.

1) My understanding is that most the "researchers" and even students at ATI have a main role at a home institution. Really the question should be something more like "did ATI funding help advance UK research generally?" not "was ATI able to claim its own successes?"

2) Nobody has really mentioned how PhDs are a little different in the UK. E.g. you propose a topic -> research for three years -> receive PhD. In the US its more like research for 2+ years -> find a promising area -> do groundbreaking work over 1+ years -> receive PhD. In other words, its significantly easier to change your research direction in the US, of course its easier to miss out on things like the LLM explosion.