Ethics, Ethnicity, and Plagiarism (an ethics question for professors)

I was recently inspired to write this after having a conversation with a fellow adjunct about the demographics of plagiarism in our ethnically very diverse school. (The discussion here inspired me to post this for discussion.) It mimics questions about racial profiling. Those who think racial profiling is OK will have little problem with the following. Those who do not might have a problem, but I think there is nonetheless a significant difference that might make even the anti-profilers think that this case might be different:

Generally when we think of treating people unfairly we presume that the innocent are in some way harmed. I take it for granted that there is no problem harming (read: punishing) the guilty. does what follows present a problem in so far as it only punishes the guilty, albeit it punishes a larger number of the guilty in some particular subgroup. (Fans of Ernest van den Haag should have no problem with this.)

What if an instructor for a number of consecutive semesters would randomly choose ten percent of the papers she received in the class and ran a few random sentences from those papers through Google to spot-check for plagiarism. This is in addition to the quite obviously plagiarized papers.

Let us say that each assignment reveals (at least) one case of plagiarism detected by random spot-checking.

Then, looking at the plagiarists she caught by this random method and combining them with the plagiarists she caught beside she discovers a preponderance of cases that are biased in favor of people whose names indicate a common ethnicity (eg, they are all French sounding).

Then she Googles all the papers and discovers that indeed there is a disproportionate amount of people of that ethnicity who
plagiarized papers.

(The reason for this is irrelevant. I suspect that there is no gene for cheating. However cultural necessity may play a role, eg, impoverished countries may force individuals in that culture to be able to get by only via dishonesty. Or perhaps, a society which makes up a large proportion of a particular college's demographic might look down on secular knowledge (thought it is necessary for a livelihood) and thus encouraging them to have fewer qualms about cheating.)

Is the teacher then justified in looking at this particular group more carefully in the future? That is, should or may, the teacher select the obvious cases of plagiarism, the random ten percent, and all the individuals from a particular sub-group already judged to be more prone to plagiarism.

The innocent in this case do not suffer. They never know they were checked, and thus never feel the humiliation associated with spot-checks. On the cheating list, the particular ethnic group will show up significantly more, as opposed to slightly more. So the guilty of one group will likely be caught more, and hence punished more. The innocent of course will never suffer.

Are there any good argument against this kind of "ethnic profiling"?