At 4:20, I removed the checker texture, and it indeed was deleted from the UV viewport, but it's still on my model in Blender Render. What am I doing wrong?
Sometimes I've seen this if not all my mesh elements were selected when removing the texture from UVs. Make sure you select all of your mesh and then remove in the UV/Image editor.
Also you can try SHIFT + clicking the X button in the UV/Image editor to remove the image from all it's connections (including to other objects if it's assigned to other objects, so use with caution)