Telling people not to look information up themselves is indeed very strange. Especially a recently diagnosed patient has lots of questions and won't be able to ask all of them at their appointments (questions coming up between appointments, questions from relatives and friends they want to answer, forgetting to ask things, etc.).
However, searching for information on health issues, especially cancer, on the internet can be problematic. There are a lot of websites around promising quick cures to all kinds of cancer, if only you eat right / use this product they are selling / stop doing a specific thing / etc. This can lead to patients doing things that they shouldn't, like discontinuing treatments. The internet site Science-based Medicine has a lot of articles in their cancer tag debunking such treatments and warning of the dangers.
A much more reasonable approach to this problem would be to provide a patient with trusted sources - pamphlets and such, of course, but also links to websites that can generally be trusted with information about medical treatment, but is accessible to laypeople, like the US National Institute for Cancer, or the Mayo Clinic. For patients a bit younger, the cancer.net website (which is a website by the the American Society of Clinical Oncology) has a list of resources for young adults. They also have information on how to evaluate information found on the internet
Health care professionals should encourage patients to discuss anything they read and have questions about with a professional. The reality of today is that, even if you tell patients they shouldn't look something up, they likely will. So it's important they know how to evaluate and deal with the information they find.
studies indicate that 16-64% of patients are using the internet to obtain health information. For the most part, patients perceive the online information to be reliable but maintain a healthy degree of skepticism. Studies objectively evaluating cancer information on the internet indicate that there is reasonable quality, although the language level of many sites is higher than that of the average American, which may limit the utility of the websites
Internet health resources and the cancer patient
If your friend wants to and has the energy to, I don't think it would be wrong to push back on this blanket policy.
Studies done regarding this subject find that Internet use makes patients more informed and helps them take a more active role in their health care decisions, which may prevent the feeling of helplessness many cancer patients experience.
Cancer patients’ Internet use for health information at wave one led them to want to be more active participants in medical decision making
Internet use leads cancer patients to be active health care consumers