You can reasonably assume that if no terms and conditions were offered, then your use of a publicly accessible endpoint is authorized.
But if terms and conditions ARE offered to you, and you bypass acceptance somehow, then you're knowingly accessing the system without being authorized.
I really doubt this would be prosecuted except as part of some much larger misbehavior, but it is there.
If I use wget to mirror a site and there are terms and conditions that I never see then I'm "using a public facing API while being unaware of terms and conditions".
I mean, the CFAA being discussed is a notoriously broad law that's far too easy to run afoul of without realizing it.It's totally possible a court could seem that illegal.
But if terms and conditions ARE offered to you, and you bypass acceptance somehow, then you're knowingly accessing the system without being authorized.
I really doubt this would be prosecuted except as part of some much larger misbehavior, but it is there.