To the oft-voiced argument 'Scotland elected one Conservative MP and has a Conservative government - this is WRONG!', my counter is straightforward.
Scotland is part of the United Kingdom. In being part of the United Kingdom, it accepts the terms of that union. In union-wide elections, Scotland has its proportional share of seats, but it obviously does not have casting vote.
The Conservative & Unionist, Liberal Democratic and Labour parties are all unionist - they subscribe to the terms of the union I described above. Thus a vote for the Liberal Democrats or Labour is a vote for a party that subscribes to the legitimacy of the union and thus the legitimacy of a Conservative government that carries the largest number of seats in the Union Parliament.
The party that rejects the legitimacy of the Union, the Scottish National Party, did not get substantially more votes than the Conservatives (who with the SNP and Liberal Democrats were all within the 400,000 - 500,000 mark), and certainly failed to come close to matching the pro-Union vote.
Thus the Conservative government of the United Kingdom derives its mandate for administering non-devolved issues in Scotland from the Union whose legitimacy has been endorsed by the vast majority of the Scottish electorate in the pan-union elections. Simple.