The way I see it, he has an accident is not a past event. The form "has" denotes the present indefinite tense. For it to be a past event, we'll have to use "had".
I feel I know what you mean, though.
He's had an accident. -> Here we might feel the event happened some time ago today.
He has an accident. -> This should imply the person has just gotten into an accident and something should be done about it right away.
The two are really close in meaning, but a native speaker would be able to tell the difference, based on the situation in which those events could take place.
Student or Learner