Rest assured, i don’t agree with it either, but as you say this seems to follow from the statement
We shouldn’t treat/cure cancer, cancer happens in nature and we’re a part of nature
We shouldn’t try to prevent rape, rape happens in nature and we’re part of nature
We shouldn’t try to limit animal suffering, animal suffering happens in nature and we’re part of nature
It’s the good old argument from naturalism
We do have evidence that at least one species give their members individual names, and at least a portion of the members understand the concept of evolution
So i would say we have more evidence for this meme being accurate than any god being real