Depending on what you’re doing with AI, I don’t think the advice needs to be this absolute, especially because we can also use privacy-respecting AI services like Brave’s Leo and Duck.ai.
What is really the difference between AI chat services and traditional search engines in regards to this? Don’t they have the same issue that you’re essentially trusting your data with these 3rd party services? At least with something like Brave’s Leo or Duck.ai, there is at least a promise that the data isn’t stored or used to train AI models, which is a similar claim that both Brave and DuckDuckGo make with their traditional search engines (Although DuckDuckGo stores your searches).
So, I would argue that when it comes to privacy, these AI services are very similar to traditional search engines, and while going completely local will always give you the best privacy, it isn’t absolutely needed if you value your privacy, and you can always use something like Tor to access these more privacy-respecting AI services if you want.