That is correct. The creator of classified information is supposed to choose the classification. That is usually inferred from the source if the information is a synthesis of existing material, and from the definitions and guidelines if the material is an entirely new creation. As Secretary of State, she could argue that she mishandled her responsibilities for choosing the proper classification rather than mishandling classified materials. I'm not sure that is any better politically.
So Hillary took the satellite pictures? Or did they come from NSA who would have put on the TS classification?