I agree - the causal link is very important to note.
In terms of born premature vs born early, I understand that premature is the medical term. As a medical student, I also understand that it can be helpful to use more precise words in describing a situation.
However, I personally think that a lot of our medical jargon is due for simplification. For example, is there really any benefit to saying "epistaxis" rather than "bloody nose", or "rhinorrhea" rather than "runny nose"?
In the case of "born early" - premature and preterm are already interchangeable. I wouldn't mind adding born early to the mix.