I understand a software development organization can be CMMI accessed
at various levels, but software is not said to be CMMI accessed correct?
CMMI is a set of processes which guide the organization, but not the resulting software.
I often hear of companies proclaiming that their software is "CMMI Level x Compliant." I just had a company tell me that they methodology, which was for sale, was "CMMI Maturity Level 5." Both of these characterizations are misleading.
You are correct - an organization is the target of an appraisal, not the software or the methods used to develop it.
To your last point, that CMMI is a set of processes, I will have to disagree. The CMMI is a model that serves as a set of requirements (or a framework) that you would use to develop your process. Using it as a process would be a disaster.