"His argument was on the lines of English being of Saxon derivation and Scots from the Anglian or Frisian language; or was it the other way round?"

The northern part of what had been the Anglian Kingdom of Northumbria (from the present border up to the Forth) became part of Scotland (ie Alba) in the early 11thC though it had been within the Scottish sphere prior to that. The dominant language in this region was the Northumbrian dialect of Anglo-Saxon as spoken in northern England also. It also had elements of Anglo-Danish. When the burghs started to grow in Scotland this language gradually became first the language of trade and eventually the language of government adding other influences (ie French, Norse and Gaelic loan words etc) which gradually differentiated it from the northern English dialects and of course the standard English which wsa developing further south.