Correct, but you said it was 7.3%, which is the revised number. So if you had said that at the time Obama took office, the official UE rate was at 7.2%, that would be fine. But you used the revised number (from Jan 2011 or later) and it makes no sense to use that number instead of the 7.8% which was the rate being collected that week.
Employment Situation for January 2009What's important is what is NOT there: an announcement of a different reference week. The reference week is only changed when the usual week is under unusual conditions and an announcement is made in the release. For example, in the Employment Situation for
November 2006 and for
November 2012 the reference weeks were the weeks that contained the 5th because otherwise the collection week (the week after the reference week) would have been the same week as Thanksgiving when it's practically impossible to do an accurate household survey.
Since the default is the week that contains the 12th, and an announcement is made if otherwise, then we can conclude that it was the week of the 12th in Jan 2009.