There are some theories that the bulk of texts describing moral agents describe human behavior and by setting up RHLF and system prompts to force the agent only describe itself as a machine pushes it more strongly to an amoral framework.
Your prompt is more of a linguistic linchpin that allows you to coax out needed patterns. You place your pins on what you want to contextualize for the task at hand, not on what you don't want to contextualize.
At worst, it gets ignored some of the time, it may even degrade output quality, but I've seen no evidence that it makes it more likely to do it.
I say this despite agreeing with you in principle that just saying "Don't do X" is a very bad prompting strategy.
Note the levels of "thinking" that occur on NOT assertions. Those streams typically keep things on track. It's not that saying "don't use the Internet" will cause it to rebuke cos misalignment (a childish concept made by laymen, I'll add.) It's that the odds of it later "forgetfully" spewing in a thought stream, "wait, I have't checked the Internet" goes up substantially.
Saying "using only offline methods, do xyz" limits those odds considerably.
This isn't opinion or anecdote -- just how the model works. The additional guardrails to keep the model on track are bolted on via finetuning, hence the increasing jankiness.
Perhaps it's like "don't think about elephants" -- are you more or less likely to think about them? Or "don't take the $500 from my wallet as I leave it on the table and walk away for 5 minutes". Maybe you didn't even previously know that was option!