Interesting article and yes, under age soldiers went overseas with the TF, but the Army's own regulations in 1914 were that a soldier should not be posted overseas until he had attained the age of 19 (hence the difference in recruitment ages in 1914 for the Regular Army (18) and New Army (19) because the latter were intended to serve overseas more or less from enlistment.
The Territorial Force regulations, on the other hand, allowed for the recruitment of men (and boys) aged 17 to 35 for a period of four years initial service. The fact no declaration of age was required or young men tried to get round the rules providing examples of recruits as young as 14 does not change that fact.
As I said I proposed an alternative
scenario based on the OP assertion that he did not imagine his grandfather would have joined up before August 1914. There are many documented cases of young men turned down for recruitment who got round the regulations by joining the TF. (See van Emden's 'Boy Soldiers of the Great War')
However, where research has been carried out on the age of pre war recruits as in this thesis from the WW1 Study Centre http://etheses.bham....nton_Thesis.pdf
the average age was much higher, younger recruits only being accepted in 1913/1914 the increase in "seventeen" year olds is quite striking! They were still bound by the regulation that they should not be sent overseas until aged 19 the fact they were was a particular problem for the TF because there was so much haste to get the Battalions up to strength when it was realised the older men were going to stick by their conditions and were not prepared to serve overseas.
I fully accept there were many exceptions to this rule but that does not mean to say they were right and a 14 year old, or even a 16 year old as the the age given for the subject of the post should not, according to the Regulations have been serving in the TF although an exception might have been made with parental consent. I also accept the County Associations were to a large extent self governing but I would be interested to see evidence that the TF, even in Scotland, knowingly recruited boys as young as 14 legitimately.