Yes, anything under the PBS has limited grounds for appeal, so unless the breached his human rights or as garry said, were racially motivated.
Without knowing all the specifics, previous income, what type of evidence is acceptable is clearly laid out. The burden to prove things is on the applicant. If he or she does not provide acceptable information, they will simply refuse the applicant. They will not required to go out of their way and call around an talk to people to prove something the applicant should have proven.
It is likely that the evidence that was submitted for proof of income did not meet the requirements, the administrative review confirmed that the evidence was not within the guidelines. The only way really to get a Tier 1 approved after a refusal is to correct what was wrong with the application and apply again. ARs only cover situations when the ECO clearly did not follow the guidance or there was discretion that the ECO exercised. There is no discretion to exercise in the PBS.