The 'framework' there, (ie: of 'incompleteness'), is flawed by inconsistency and so is ultimately philosophically incompatable with the scientific method. This is a commonly held misconceived philosophy of science.
I'm not sure what you are saying here. ID people do seem to be saying that methodological naturalism is incomplete. From anything I've seen, their statements aren't flawed by inconsistency (unless one assumes methodological naturalism) and not necessarily incompatible with scientific methods (there is no 'one' agreed upon scientific method, as Scientific American discussed a few years ago).
However, I see several major problems for ID people. Their ideas seem to have problems not sounding a lot like god of the gaps arguments, designing experiments and getting evidence that would decisively support an explanation of intelligence, and following many of the non-methodological naturalist assumptions of scientific theories. The current way science is done using a conservative approach by applying methodological naturalism and the different types of scientific methods seems to work fine. I followed the ID movement closely for years and they produced very little useful science and a lot of philosophical musings, political activism and noise - not much more.
'Statements of nature' are statements for informing ourselves (collectively) of the meaning of the term: 'nature', in that sense, we are informing ourselves about our own perceptions/observations. There is no need to say 'what exists beyond' those perceptions/observations - they are our reality. This interpretation restores the consistent basis for the establishment of knowledge of what 'nature' means, in science.
I wouldn't agree here - perceptions are faulty. In science you talk about third person perspective, as first person perspective are unreliable. Observations that are too closely related to first person perspectives introduce all kinds of biases. The value of science is that, when done correctly, can lead to observations and information that is independent of the observer. This is what establishes a consistent framework for understanding what we mean by reality (or nature)
The other interpretation (ie: 'incompleteness'), is an artefact of philosophically held beliefs in Realism - which should be ignorable in properly conducted science .. (and it is).