A tale of two Flynn's - Clonbur to Pittsburgh

Bottom line up front is that I'm seeking help to establish a relationship between John Flynn (1862-1912) and Catherine Flynn (unknown-1961).  Additional question, are John Flynn (1815-1899) and Catherine Morrin (1821-1906) the parents of Catherine Flynn (d. 1961) and John Flynn (d.1912)?

BACKGROUND:

Clonbur native John Flynn died aboard the Titanic in 1912. John had emigrated from County Galway to Pittsburgh, Allegheny County, USA but had returned from there to Clonbur in early 1912 to help his sister, Bridget Mannion, following the death of her husband.

I recently discovered a DNA match(s) between the descendants of John Flynn(d.1912) and my family. My 2x great-grandmother is Catherine Flynn who I can first document in Pittsburgh, PA, USA in 1894 due to her marriage to John Flanagan.  

My hypothesis is that Catherine Flynn is John Flynn's sister. I base this hypothesis on two facts summarized below.

One, I found a birth record for Catherine on Irish Genealogy.ie from Carrowhakeen townland on 15 Jun 1868. I'm noting the fact that the parents, John Flynn and Kate Morrin, listed on the birth certificate of Catherine in Carrowhakeen townland are also the names listed on Catherines death certificate issued by Allegheny County, PA in 1961.

Two, the DNA shared matches between the descendants of John Flynn (d.1912) and the descendants of Catherine (d. 1961) and her two husbands in Pittsburgh, John Flanagan and Owen Gallagher.  The fact that descendents of both marriages match to the descendents of John Flynn help pinpoint Catharine as the pathway and not the ancestors of her husbands.

The hypothesis can be disproven if it turns out that, as reported in a 10 April 2012 Mayo News article,  John Flynn (d.1912) had only two sisters, Mary and Bridget.  There may be additional ways to disprove this hypothesis.

If the sister/brother hypothesis is wrong I would begin to pursue the hypothesis that John and Catherine are cousins as both have birth records in the Carrowhakeen townland.

Thanks in advance for your insight and analysis!

-Cheers,

Chris