This is one of those funny subjects where it is easy to overlook the obvious.
Lets consider popular American views of the Irish in the mid-late 19th century. At that time they were thought of as no better than the "plantation darkey." Because Irish is "cool" now, it we often ignore the reasons why these characteristic "Irish" pieces were included in the tudors, written by folks who made money by smearing burnt cork on their faces.
The "Irish" bit was a part of the cork opera, complete with bright red wig, beard, and green suit. Paddy was a character the same as Jim Crow or Tambo. He would tell limericks, be drunk, and try to fight.
These tunes were more likely included for "Paddy" to dance a jig rather than a nod to the noble legacy of traditional Irish folk music.
Were they just as authentic as the "true African" music also in the tutors or were they a gross exaggeration and eventually picked up by the Irish in America?
These may or may not be true representations of Irish music in the mid 19th century. I don't know. I do know that they are "Irish" tunes in the minstrel show sense.
I thought I'd add my two cents worth to this discussion. Yes, the Irish were cruelly lampooned in the mid-19th century in much the same fashion that blacks were lampooned. However, the Irish contribution to early minstrelsy is indisputable. First, some of the top performers (Sweeney, Emmett, et.al.) were at least nominally of Irish descent. Second, the Virginia Minstrels (and other troupes) toured extensively in Ireland and Scotland in the mid-1840s and, presumably, absorbed as much of the local performance culture as they contributed to it. Most important of all, the audience for minstrel shows in places like New York and Boston was mostly white working class and, by the 1850s, a large portion of that white working class was made up of immigrant Irish. My guess is that not only the minstrel's musical repertoire, but their associated dancing, had strong Irish elements.