the problem is that if you steal the weights then you can serve your own gpt4, and it's very hard to prove that what you're serving is actually gpt4. (or you could just start using it without paying ofc)
None of the siblings are right. The models themselves are idempotent: given the same context you will get the same activations. However the output distribution is sampled in a pseudorandom way by these chat tools. You can seed all the prngs in the system to always have reproducible output using sampling, or even go beyond that and just work with the raw probability distribution by hand.
That's the feature of chat - it remembers what has been said and that changes the context in which it says new things. If you use the API it starts fresh each time, and if you turn down the 'temperature' it produces very similar and identical answers.