The level of risk is probably the most subjective of all the elements used in auditing an E&M level so this is not an easy answer. I frequently refer coders to the statement about risk in the CMS guidelines: "Because the determination of risk is complex and not readily quantifiable, the table includes common clinical examples rather than absolute measures of risk. The assessment of risk of the presenting problem(s) is based on the risk related to the disease process anticipated between the present encounter and the next one. The assessment of risk of selecting diagnostic procedures and management options is based on the risk during and immediately following any procedures or treatment." I think this is useful because it shows that risk is not just tied to a particular diagnosis, but rather is a measure of the provider's assessment of the patient's condition at that encounter, and so this is information that should be reflected in documentation in addition to the diagnosis.
You've said the provider documented that the patient's status is 'fair', so I think your question as to why this is a high risk patient is legitimate. But since an accurate assessment of risk can involve clinical measures that a coder is not trained to interpret, many coders/auditors I've encountered will defer to the provider's judgment for the risk level. And in cases where the auditor assesses one level of risk and the provider another, auditors will often use it as a starting point for a discussion rather than citing it as an error, and I think that's the best approach. It's an opportunity to review the guidelines with the provider and have them give you input as to why, in their clinic judgment, they feel the patient is high risk, and for you to explain to them why the documentation, to an auditor's eye, does not support that.
I'd also make a reminder that risk is only one element of MDM and that for high level MDM, the documentation also needs to reflect either extensive number of diagnoses and/or extensive review of data. In your example, you've said the patient is improving, so unless the provider is managing more than 3 problems or reviewing extensive data, then the designation of high risk would be something of a moot point as it would still not result in high level MDM.