Is it true that headhunting companies and bosses are mysteriously recruiting people without telling the company before the interview?

It's hard to say. It may be a liar or it may be true.

If this headhunting company is famous, you can try it; If the popularity is not high, if you want to try it, you can talk about something that is not sensitive and confidential, and you can go in and out.

You can't show your sword easily unless someone else shows their cards.