So, either the family group in 1891 Coatbridge are a red herring, with same/similar names and origins or, as is quite possible, the Owen/Hugh Hughes of the opening post, is the one born in Coatbridge and for whatever reason, used incorrect birth details and more or less stuck with those throughout his time in America.
Birthdays did not have as much importance placed on them as nowadays, with many not knowing their correct details. Years often vary in later documents, even day/month. 17th March, as in Owen/Hugh's case, if not his actual birthday, could have been chosen as an easy to remember significant day (ie St Patrick's). If he was, as you have suggested, brought up by extended family relatives, they could quite easily have forgotten which of John and Mary's children were born in County Armagh and which in Scotland, so unintentionally led Owen/Hugh to believe his birth was County Armagh, and also, if they had no access to his birth registration, may have been unsure of the day/month and misled him on this too.
You need to go step by step through your research again, cross referecing the various finds, and seeing if there is anything to rule out the Scottish born Hugh as being your Owen/Hugh, the obvious example being if you can find the Scottish born one still in Scottish records after your Owen/Hugh has emigrated.
. (His mother passed away when he was about 9 and he was supposedly sent to live with relatives for some time if that helps...)
In addition, consider that the 1901 census family group in Coatbridge, posted earlier in this thread by Monica, which seems to possibly be the same family as in 1891, has that Hugh still with his own father/siblings, albeit you only said your Owen/Hugh was sent to relatives for 'some time', so he could quite possibly have been back with parent/siblings when older.
You said your Owen/Hugh married in Coatbridge in 1914, so do you have him in 1911 census? Certainly, as you will know, he was already using Owen at time of his December 1914 (registered in January 1915) marriage:
BENNETT
JESSIE
HUGHES
OWEN
1915
651/ 13
Airdrie or New Monkland