The 1911 Carrickreagh Armstrong census record on the NAI website has been wrongly (but understandably) transcribed as William Armstrong, the actual census return shows
Wilkin Armstrong, which turns a relatively common name into something much less common and begs a potential relevance to the mention of Wilkin in the OP (maybe the family anecdote got mixed up over the years?):
http://www.census.nationalarchives.ie/reels/nai002319659/Wilkin Armstrong married Emily Spratt in Trory Church of Ireland (just outside Enniskillen) on 14 December 1904, his father was James Armstrong and hers was Jack (John) Spratt. GRONI online has the civil record for the marriage if required.
Civil birth records are also available via GRONI online for children David Armstrong b. 1 October 1905 (the RootsIreland website transcribed record is for David James Armstrong), Elizabeth Armstrong b. 19 July 1907 (the RootsIreland website transcribed record is for Elizabeth Emily Armstrong), John Armstrong b. 11 October 1909 (the RootsIreland website transcribed record is for John Dickson Armstrong), and Wilkin Armstrong b. 9 January 1912 (the RootsIreland website transcribed record is for Wilkin Hicks Armstrong), all registered at Enniskillen.
The RootsIreland website index also indicates there are transcribed birth records for Mary Armstrong in 1914 (to parents
William Armstrong and Emily Spratt), and William Robert Armstrong in 1916 and Francis Armstrong in 1920 (to parents
Wilkin Armstrong and Emily Spratt). All registered in Fermanagh (Ely Registrar's District).
GRONI online and RootsIreland record content is pay to view, but you can get a lot of information from just searching the indexes.