There’s alive, and there’s living. It’s possibly for someone’s body to be alive even though the person is completely and forever gone.
Not saying that’s what happened here, only that someone appearing to be looking around doesn’t necessarily mean there’s a person inside that body choosing to do so.
Personal source: I saw a beloved family member appear to look around, even while an EEG showed that there was zero activity in the parts of her hurt brain that we’d think of as “her”. It’s terrible to behold. But yes, it can also be just a common reflex.
(I have zero intent to defend the hospital. I’m replying to that 1 specific thing you said, but am absolutely not saying the hospital was in the right.)