This points to a larger discussion about systems thinking. Specifically that warning labels put responsibility on the individual to correctly read, interpret, and act on information in the label. Alternatively, consider not using a label and fixing the underlying systemic problem so that there is no danger in the first place. In the case of a lawn mower, this is designing it such that it doesn't require a human to operate it correctly. It fails to operate if used incorrectly.
Given this is HN, the equivalent in software is: fix the code on your side; don't try to train your users. We don't add warning labels telling users to not do SQL injection, we solve it systematically by making sure our backend isn't using untrusted user inputs directly in queries!
You're right in that warning stickers won't fix stupid, and that we need more systemic action in order to treat the cause and not the symptom. I'll be honest: I don't even know what that systemic action would be in the case of misinformation on Twitter, but I know that warning labels are just a way to shunt responsibility away from Twitter and onto individual users.