had/met with an accident.

He had an accident. He was knocked down by a car.

Both are used, T, but 'met with' is a bit literary. In the right context even had met with an accident could be used.

I think it could be more complicated than that.

As in:

He had an accident. (He spilled hot coffee. He did this himself)

He met with an accident. (A car hit him. This was done by somebody else)



But maybe I'm looking for complications or nuances when there are none.

"met with an accident" is the correct usage.