The Eye Witnesses: Conclusion
On the basis of this web information, chronological discipline, and logical inference (based on extended teaching experience), it seems likely to me that we can treat the sources this way:
Reasonable description of Babylon, has no bearing on the existence, appearance or attribution of the gardens
Historical conflicts with other Greek historians (such as Herodotus) probably caused by his unexpected political loyalties. Structurally logical description of the Hanging Gardens
Greek historian who is generally respected, but his description of the Hanging Gardens is muddled and contaminated, and therefore probably unreliable
We have perfectly good reason to believe that the Hanging Gardens existed, and we have a good description of them from Ctesias.
We have not yet established who probably built them—that is the subject of the next section.