As I discussed last time, ethics is not an exact science that provides testable hypotheses, well-defined causation, and precise measurements. So what results can ethics legitimately provide, and on what basis? Despite Rand's protestations, Aristotle's conclusions were not all that different from hers: ethics defines general principles based on fundamental facts about human nature, but they must be applied individually based on the particulars of one's psychological constitution and life experiences.
For Aristotle, the most fundamental fact about human nature is that the work/function (ἔργον) or means of life (ζωή) or characteristic way of living (βίος) for human beings is reason (an argument closely paralleled by Rand's claim that reason is man's only tool of knowledge and basic way of survival; see my essay A Philosophy for Living on Earth for details).
It is true that Aristotle pays more attention to common opinions about ethical matters than Rand does (see for example 1098b27-29); however, he uses such opinions for corroboration, not for proof, on the assumption that "all the facts are linked to the truth" (1098b11). It is also true that he pays special attention to the opinions of ὁ σπουδαῖος (a person who is serious, earnest, zealous, good, excellent, of strong character), for example at 1099a24; but this is because the function of ὁ σπουδαῖος is to perform the characteristic activity (ἔργον) of a human being especially well. Thus for Aristotle there is a line of causation from the fundamental human capacity for reason to the definition of excellence, and his ethical arguments are not limited to that which was conventionally considered to be noble and wise in his time.
Leaving aside her misunderstandings of Aristotle's methodology, Rand might have had any number of reasons for disagreeing with the substance of Aristotle's ethics. Most centrally for Rand's purposes, he dismissed out of hand the ethical value of money-making, business, art, technology, and productive activity in general (preferring instead a life of contemplation or, secondarily, a life of what nowadays we would call public service). Yet given that Rand also thought that the fundamental value of productive activity was not demonstrated historically until the Industrial Revolution, it would have been difficult for her to hold Aristotle to account regarding the centrally organizing purpose of the best life for human beings. Apparently it was easier for her to criticize him on methodological grounds, misguided as those criticisms were.