'this' one that we have been talking about? I don't know. Perhaps an English speaker wouldn't.
We have to keep the direct translation of "ten" and "tamten" consistent, so that's why the main translation of "tego wypadku" will always be "this accident", with "that accident" and "the accident" being accepted. Sometimes it will result in unnatural English sentences, but if we weren't consistent, everyone would get totally lost.