Tyranny always has public support. The evil wizard lord of a kingdom scenario has never and will never occur in reality - someone despised by everyone cannot come into power... That doesn't mean the tyrant has the majority of public support, but I'd find it hard to believe any tyrant has less than 30% when coming to power.
That said, your point is important and something many people don't seem to understand: those foreign leaders we in the West like to describe as tyrants, dictators, despots, strongmen, etc, are generally at least popular at home, and often adored.
Lastly, popular support is from the factions, not the people - in medieval europe most of the people had no factional representation politically, all the power had been entirely concentrated in the various estates.
1. See Lord Vetinari in like every discworld book ever.