Yes, you are right, this is caused by the editor and is difficult to solve.
EXPLAINATION :
When you choose an image in com_media popup (image picker), the response callback funstion is :
jInsertEditorText()
To get the result and populate image previews, JDom write this function to catch the result.
BUT, the editor is doing the same for it's owns (To insert images in the text)... And write this same function.
So the conflict occurs and you cannot solve it easily.
While Joomla core does not permit this, Cook will not be able without hacks.
Clean solution : separate your forms or don't use these two in same form.
No issue possible for the moment and it is not a Cook weakness.