There was one black female mentee who I noticed was timid in taking credit for her work. I had recently attended a diversity panel where someone in a similar role as me said that in a similar situation, and her advice to her mentee was "Think about what a white man would do" and everyone applaud such an insightful advice. So identifying such an opportunity, I said the exact same thing word for word, basically "I see you're hesitating to take credit for your work. Think about what a white man would do."
Immediately after saying that, I could tell it wasn't taken well, and she asked "what does that mean?" I couldn't come up with an answer for that which wouldn't be taken in a really bad way, so I backpedaled. She later reported me to an administrative person who luckily felt it was too vague to file a serious report about, but told me to watch what I say.
But I do have a solution (my trick). From that point on, I definitely give more subtle advice unless they have passed my test, which is I see how they react to situations where they could give the benefit of the doubt to others in vague situations. Sometimes, I'll bring up a past story about another anonymous person and see if they are outraged and want to get them in trouble. Only the ones who remark that they probably had good intentions, and don't react too strongly, I'll give more candid advice to.
What was wrong with a "be bolder"/"be more assertive"/"don't be afraid of taking credit for your work"?
I don't see those as useful since it doesn't provide the person any actual guidance or reference point. What does assertive mean? What should I exactly do? How do I do it? "Act like X" provides a well known reference point that they can use to adjust their behavior based on. They can remember all the times they've seen X do something in a similar situation and then just act like that.
If you want to make it super explicit, come up with examples. "Be bolder, for example for this project I saw you doing 80% of the work, you should get to headline the presentation and have top billing on the authors page".
"Act like X" is also potentially useful, if you make it explicit. Explicit is not "Act like a white man" (whaaaa?). Explicit: is "Act like Bob, for example do you remember when HR said he couldn't have a new screen and he insisted"?