There are three kinds of data now, synthetic, pre-2022 and current. Everything pre-2022 is definitely written by humans, synthetic data is still synthetic, and post-2022 is a mix of both.
I wouldn't be surprised if "AI detectors" work somewhat for this use case. They're biased, far from accurate and a terrible idea if you need to make important decisions (like whether to expel a student for cheating), but there's quite a large room for errors here.
I'm not sure if methods like article spinning counts as written by humans. This is something you could automate before AI and it would take a human written article and randomly swap words with similar meaning throughout to make it seem original.
Many historical English-language news reports published on the English-language websites of foreign news media from non-English-speaking countries, from 1998 (Babelfish era) to ~a few months ago, may be unreliable training data for this reason.
I copied a prompt translated from spanish to english using ChatGPT Plus in a GPT-4o Azure OpenAI Service endpoint. It did work in Spanish but didn't run in english because the default AOS Content Filters detected a jailbreak intent. It was quite weird.
If synthetic data is mixed into your upstream data sources in a way you cannot control, then your ML team loses a valuable controllable parameter.