I'm not a lawyer and I haven't studied the relevant laws, but I'm quite skeptical that trademark and publicity rights align with a broad prohibition on using the names of copyright holders to "endorse or promote" without "specific prior written permission". That phrasing could be interpreted to prohibit, for example, giving an interview about your derived work, and making the factual statement: "It's based on software called Foo, which was written by a guy named John Smith." No endorsement is implied, but you are using John Smith's name in an interview which is perhaps intended for promotional purposes.
Even if this restriction does align with US law, I will be flabbergasted if it aligns with the laws of every other country as well.
I'm quite convinced this clause says you cannot make it seem like the original authors endorse your derivative product, the BSD license is so widespread I would assume if your interpretation was correct we would have seen many issues by now, but IANAL too. I do hope you are wrong :-)
Even if this restriction does align with US law, I will be flabbergasted if it aligns with the laws of every other country as well.