Cahill great grandmother born in Limerick not Tipperary?

My great grandmother Margaret Cahill was born on Dec 14 1869 as per her obituary also showing she was born in Tipperary, Ireland in the obit.  My problem is that when searching for birth information only two december births were listed in family search for margaret in dec of 1869. One was not an exact match but very close on Dec 12 1869 but was in Rathellen, Carlow, Kildare and Queens, Ireland. The other was an exact match of Dec 14 1869 born to Bridget Cahill and shows Limerick No. 2, St. Munchins, City of Limerick, Ireland. That is probably the one but she always told her family that she was born in Tipperary. I know that is close to Limerick so maybe she never knew she was born in Limerick or this isn't  the right one. Anyone have any ideas on this? thanks!