Nobody promises that AI will cure diseases. This article was misleading. An earlier WSJ article wrote:

A letter at the front of the filing says AI could speed up biology and medicine, “potentially curing diseases that have plagued humanity for millennia.” It names cancer, Alzheimer’s, heart disease, rare genetic diseases and infectious diseases as examples.

Anthropic said AI could speed up, and potential help with curing diseases. Not that AI would do that by itself.