They do different kinds of mathematics. Tao works mainly in analytic number theory & that's why he got a Fields medal. Hamkins works in foundations of mathematics, logic, & computability theory.
For the sake of rigor it appears he found it interesting that someone else found them helpful in the past rather than "Terry Tao[himself] has found them helpful in the past."
> This was one further addition to a recent sequence of examples where an Erdős problem had been automatically solved in one fashion or another by an AI tool.[Aristotle] Like the previous cases, the proof turned out to not be particularly novel
He concludes:
> One striking feature of this story for me is how important it was to have a diverse set of people, literature, and tools to attack this problem. To be able to state and prove the precise formula for {c(n)} required multiple observations
Which looks like he wants to focus the praise for the solution on the "diverse set of people" relegating any "praise" for LLMs to the obfuscated and ambiguous category of "tools" behind literature.