The 1871 James McKenzie was, according to the transcription, a new recruit to the 93rd, who had joined at Forres and who, when the Army Worldwide Index was collated, was at the depot in Inverness, presumably awaiting training. The index is collated from a multitude of sources and one would be hard pressed to get to the original source except in one case that you might like to chase down? One source was the 1871 census so a James McKenzie in a barracks in Inverness is the target!
As to whether a soldier could be recruited for the 93rd in Edinburgh, undoubtedly. The local connections, pre the 1881 reforms, played much less of a part in the process, even for the highland regiments who recruited all over UK. It was done by "roaming" recruiting parties who set up in some building or another to entice men into their regiment (although family ties sometimes came into play). Look at the other James who came from Dundee and served in a Durham regiment. The 93rd were stationed in Aberdeen at the beginning of 1871 and moved to Edinburgh in July/August so perhaps they had been recruiting there earlier? They served in UK (including Ireland) throughout the period in question.
To really clutch at straws, one could note that one of the most common terms of engagement to the army was a twelve year commitment, 7 years with the colours (full time, in uniform wherever the regiment was stationed) followed by 5 years on the reserve, out of uniform in civilian life but committed to recall in the event of war. A recruit in 1871 on such an engagement would take his uniform off in 1878 which is when the man in Ireland is reported to have "finished" his service.
Perhaps one last fling at the military side could find the recruits place of birth in the 1871 census?
I have separately suggested to benchurian that all the jigsaw pieces that relate in anyway to the My Heritage man should be swept from the table and the remaining information reviewed, starting from anything known to be solid.
maxD