What part of the second statement is wrong? A turtle cannot survive without its shell, just like you could not survive without your skull. It is an intrinsic part of what allows it to function as a living organism, therefore the line between "turtle" and "shell" is a bit blurred
I mean yes, no one, human or turtle, can survive without the ecosystem of the earth, so you could really argue that the planet is the true organism and we are simply byproducts of its existence
Where can you really draw the line? Could you survive in space without any air or equipment? Even if you could, where did the equipment and air come from?
Photosynthetic organisms are for all practical purposes part of your lungs
Me needing something doesn't make that thing me, right? I need the sun to survive but neither the sun is part of me / I am part of the sun. Like, are you your skeleton? What about the other parts that are not bones then?
I think the right analogy would be to say "you are not inside your skull, you are your skull". And I would count this as a more or less correct statement.