Scrrrreeeeecchhhhhhh............thud.
(That's the sounds of goalposts being moved by you).
Prime Ministers in the UK are nominated and chosen via a vote. It's the oldest parliamentary democracy in the world.
Abhisit came to power as a result of a vote by elected members of parliament. So there was nothing illegitimate about his ascendency to power.
However, what transpired in the months/years before that is a whole different discussion.
Do you understand now?