Right, oracle machines are - or can be interpreted as - interactive. However, whatever it is that oracles do - it's often called "hypercomputation" - they're not doing computation, in the sense that Turing used the term in "On computable numbers...", which is why Turing couldn't prove that they are more powerful. The apparent - to me - problem here is that people use a definition of "computation" which is different from Turing's (which is alright), and then say that Turing was "wrong" in what he said about "computation" (which is not alright).

I actually think that operating systems are a good example of how interaction can be less powerful than algorithm - the "oracle" in this case might be a user, and the user might be new to computers, so that in this case the result of the interaction might be worse than if the "oracle" were another (non-human) computer, the interaction with which might in turn give a worse result than if you were the "oracle".