These types of statements are hard to take seriously. Those tools are remarkably good for what they are, and the fact that they can help me understand texts in foreign languages is amazing. But indistinguishable from a professional native translator (which I take it you mean, being a language native is not enough to be a translator) is something else entirely.
If you really believe that, why not recruit a professional, do a blinded study, and if it's really industinguishable you can probably get a nice publication somewhere. AI companies are flush with cash and will not think twice about sponsoring such a study.
I use these DeepL and Kagi Translate to sell products and do complicated deals with people whose language I don't understand. None of them have ever said anything to indicate that the writing is sub-par, and we sometimes have very long e-mail chains to iron out details.
I have in fact had professional translators look extensively at AI translated material, and their verdict was that the translations are perfectly fine but maybe that the AI sometimes expresses itself in a funny or strange way. Well, that's what people do as well.
Maybe it's not indistinguishable from native, but it's indistinguishable from a person who is fluent in the language, and that's the only thing which matters. Because the purpose is to communicate.
The trick is to first write in your native language in a way that is extremely clear and devoid of any risks of the receiver misunderstanding any part. This works best, whether the reader is another human or an AI translator.
This is emphatically not true in case of DeepL in my experience. I haven't tried Kagi but I wouldn't be surprised if they are using the same LLM that powers their assistant for it.
Also, this kind of claim is meaningless unless you specify the language being translated, because quality varies widely depending on that, even across popular languages, never mind small regional ones. If you try to translate, say, to Chechen using GPT-o3 or Gemini 2.5 Pro, don't expect that translation to be accurate or even grammatically correct.
