No, but they are made by animals using plant material - and are not human - hence it is natural.
From the Oxford English Dictionary, but you'll find Cambridge and Merriam-Webster to hold the same distinction:
Nature
Noun
1 [MASS NOUN] The phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations.
Natural
Adjective
1 Existing in or derived from nature; not made or caused by humankind.
Artificial
Adjective
1 Made or produced by human beings rather than occurring naturally, especially as a copy of something natural.
As I said before, the very definition of the words is what separates humanity's actions from things defined as natural. The words separate our actions from those of anything else, right or wrong or whatever the intention, that's just what the definition is. The issue is that people seem to adjust what the definition is so that Natural = Good and Artificial = Bad.
Yes, we are all part of the same system and what makes our actions separate from those that happen in nature is in the definition of the word.