"On 03 Feb 2004, Bob Cunningham wrote"
(Note that "née" is an error here, as caught by Aaron Dinkin. Heinz was not her maiden name, but a previous married name.)
"My immediate reaction was that of your lady friend ... they were talking about. But it's obviously a bad construction."
Yes, "who was born in Mozambique" is not just a dangling antecedent; it's an antecedent that falsely seems to have a back reference in "her father".
A parallel example is "Flying over the jungle, a family of gorillas was seen".
(What's a better name than "back reference" for the thing an antecedent is the antecedent of? "Anaphora" seems close, but not close enough. "Complement"?)
"My first reaction was that of Harvey, but I am not a native speaker. To me, it sounds as a ... ambiguity, as in Spanish: "NacidA en Mozambique, su padre fue un médico portugués." Maybe the speaker was reading a translation."
That's an intriguing possibility, but it doesn't seem to hold here. The remark was read by one of the regulars on the "60 Minutes" TV show. The text was written by whoever on the staff writes the things the people say. There's no reason to think it could have been a translation.