Well, I'd like to express my opinion about that.

выспаться - to have a good long sleep, that's all, it doesn't ever imply that you lack some sleep time recently.

BUT there's another derivaty of the verb спать

отоспаться - this one really means to have a good long sleep and get rid of tiredness, weakness, the state of being sleepy etc which you have because you've been lacking sleep either just today or for some longer period of time