I think you are a lawyer, no? If I'm at a cocktail party, and I meet someone, and they say, "I teach Con Law at the University of Chicago School of Law," without further elaboration, then I assume they mean "Constitutional Law" which is a class that all lawyers are required to take as 1L's (first year law students) and which are taught by full professors, not adjunct or part time professors. I don't assume they mean a seminar on voting rights, or race and the law, or whatever, which are elective courses usually taught by part time professors. If I found out the truth later, I would assume that this person was trying to trick me and impress me by giving an impression that they were more important at the law school than they really are.
That link doesn't actually say what the courses were that he taught. It just uses the general language which is misleading. When I did the research, it turned out that he did not teach Con Law. Granted, it is possible that my brief Internet research is wrong. But, the link you provided does not say that I am wrong.
Also, I said he was in office for a year before he started running for president. Maybe it was 18 months.