I’d say they’re right: cursors are way better for an API. Pages are way better for a person. This here is about an API.
1. APIs consumed by other backends lets call them API2B
2. APIs consumed by frontends lets call them API2C
In this case cursors are better for API2B but not for API2C as in case of API2C most users expect to be able to jump directly to a specific page.
At least when I am designing an API i take different decisions based on this split. For example in case of API2C I always want to see FE design even if I work on backend.