It has all but the first year it was awarded. That year (1969)Havlicek (Celtics) got robbed - his team won - but they gave the MVP to Jerry West, who played for the losing Lakers! So in all GOOD conscience - the NBA can and HAS given it to the best player on the losing team!
Meaning - the NBA screwed up and a precedent was set so that it can be given to the best player - even if on the losing team!
It happened once - therefore it can happen again!