It is an interesting site that you have given a link to, I discovered it fairly recently and admit that I do keep on going back to it but there are a few general statements on it that are not quite 100% correct.
Certainly I understand that one company of the 6th Kings ( Liverpool Rifles ) had a lot of former members of Merchant Taylors School Crosby OTC in its ranks.
There is a book "Citizen Soldiers- The Liverpool Territorials in the First World War" by Helen McCartney which looks at the 6th and 10th battalions in some detail including the social background of its members.
If you look at the list of members of the Liverpool Scottish who were commissioned in WW1 in Hal Giblins book"Bravest of Hearts" you will see that a lot of the rank and file in the Liverpool Scottish would probably have been officers in other units.
I do know of a book on the Insignia of the Liverpool Volunteers and Territorials, if of interest ( sorry couldnt resist putting that in )
http://www.sellmymilitaria.com/site/...ets&Itemid=477
P.B.