Both 'was met' and 'met' are in the simple past tense of the verb 'to meet'. The difference is that 'was met' is in the passive voice and 'met' in the active voice.
A native speakers would use the active voice, 'met', in this context.
The passive voice is usually only chosen to show the action of the verb happened to the subject of the sentence, rather than something the subject chose to do.
The expression 'met with an accident' is idiomatic and already shows the accident happened to them, so there's no reason to use the passive voice as well to be clear that is what happened.
Compare your sentence with these two:
The man shot the rabbit.
The rabbit was shot by the man.
They mean the same thing, but note how changing from the active to passive voice requires the switching of the subject and object of the sentence.
If you follow that logic, these two sentences would mean the same thing:
The man met with an accident.
An accident was met by the man.
The second of those has no logical meaning, and from that you can conclude that the meaning of the first is idiomatic.
I hope this helps. It's not an easy one to explain.