There is a tension between the “personal brand” and the brand of the larger entity one works for.
It is especially true for interns. The intern has essentially agreed to work for free to “pad their resume” or, in other words, build their personal brand.
For people of certain skill-sets, the “personal brand” is less important. If you’re an engineer, or a student of another applied science, you can present lab work and other concrete examples of work you have done or participated in, and be judged on that (often you already have been, if a study is published and peer-reviewed).
But those who fall into a more “artisinal” category (designers, journalists, artists), people whose work is both becoming excessively commodified (“oh anyone can write/throw a webpage together/et. al.”), need a portfolio that clearly displays their skills to acquire work. With these areas becoming increasingly free-lance, it is even more critical.