Depends what you want to afterwards OP.
If you intend to go work for a company as a Data Scientist or some shit then
>>10859279 is right.
However, there are some companies that develop products based on ML and for those jobs you need more than just importing a pretrained model. You also need to know how the training algorithm works, including the math.
If you intend to keep doing research in ML, then PhD in Stats or CS is fine. If you prefer to do some ML research and apply it to a certain field than probably CS PhD is the way to go.
