Hi Rebecca,
I have checked the file( 161191306) at my end and noticed that it is an Ai file.
I agree that when you open up the file in Illustrator, the file has been created with a lot of groups in it. You may get the individual layers of the file by expanding it or ungrouping it. You can go to Object> click on ungroup> and the individual layers are created. However, the file is created in such a manner by the creator that it is not possible to insert an image in Illustrator. You will have to place an image and can edit it or rotate it according to your appropriate needs by going to "Effect" option and clicking on 3D and then "Extrude and Bevel".
To open the file in Photoshop with layers, please follow the steps.
Firstly, open the file in Illustrator> Export it and save it as .PSD file> Now open it in Photoshop> It will display the layers.
Now you can Place the image by going to the file menu> click on the place as the embedded option under the file menu> select the image you desire> Go to Edit and click on free transform/ type CTRL+T> then drag and place the image in the desired rectangle by pressing the shift command.
Hope this helps!
Feel free to update this thread in case of any additional questions.
Regards,
Twarita