The origin of this myth stems from the confusion between single tenant and a multi-tenant solution. A multi-tenant solution offers a single code base to multiple clients. In some cases, the database is common but data itself is effectively segregated based on the customer account. The architecture of this type of solution does not allow an option for on premises.
JD Edwards, on the other hand, is a single tenant solution. You can implement it on premises or host it at a third party location (including Oracle Cloud). The data is never co-mingled and the codebase is not shared with other customers. This means that you have a choice of implementing JD Edwards either on premises or in the Cloud.
There are pros and cons of deploying a common codebase across all customers and is a subject of a separate conversation. Essentially, SaaS (Software as a Service) is a commercial model, generally applied to Cloud-based applications, however, it does not guarantee a Cloud ready solution.