Re: Proof, (if it were needed)
To be fair Scottish Gaelic was never the only language in Scotland. Scots was also a major language, coming from the same Germanic root as English but NOT being English. Scottish-English is English with a Scottish Accent, Scots is a Scottish language.
Gaelic is actually an Irish language, more imported than Scots. Before either of those a language from the Brittonic family of Celtic languages (rather than the Gaelic family) was probably dominant.