How much background material do beginning graduate students need to master?

I am working with a graduate student beginning research and she has asked this important question. I don't think there is a simple universal answer.

Background material includes review articles of a field, details of an experimental technique or computer code, details of derivations, seminal articles on the topic, ....

At the UQ condensed matter theory group meeting, we had a brief discussion about the question.
Answers from students, both beginning and advanced, were helpful. It also underscored how important the question is because students really do struggle with this issue. One shared how he developed some mental health problems because at the beginning of his Ph.D. he was too obsessive about understanding all the details. The question and discussion underscored to me how we need to have more discussions of this nature.

Beginning research is a difficult transition for most graduate students. When they were undergraduates they often could understand all the details and work through all the derivations.
(They are unlike a significant fraction of undergraduates who just don't seem to realise that the details DO matter.)
However, the painful reality is that what was possible for a gifted and motivated undergraduate is simply not possible for most Ph.D. research.
Research fields are so vast and have so much foundational material a student simply does not have the time to check everything and understand everything in full.
The question is painfully relevant in Australia because Ph.D. students do not do coursework (or a Masters degree) and the government continues to reduce the number of years of funding.
Furthermore, the "publish or perish" culture puts pressure on students and advisors to be cranking out papers, which means there is pressure for students not to ``waste time'' on slow and deep learning of background material.

Like many things in life, I think answers to the question require some balance and need to allow for differences in personality, learning styles, personal goals, and nature of the research topic.

Here are some composite pictures to illustrate the extremes and the associated problems and potential.

Sanjay loves to understand and master details. He is also interested in the big foundational questions the research might address. When he reads an article he likes to work through all the details of the mathematical derivations. He would prefer to write his own computer code so he really knows what is going on. He has a large stack of papers on his desk, waiting to be read, consisting of many of the papers related to his research topic. After a year he is still learning background material. However, in his third year, he has a big breakthrough because he realises that one a key assumption/derivation in the field is wrong in certain cases. He not only corrects it but opens up a new avenue of research.

Priya just wants to get on with research and is not a detail oriented person. Following her advisors request she reads a few background articles superficially and dives into research. However, she does not really grasp the big picture or understand the limitations of the technique she is using. Consequently, she wastes a lot of time making mistakes, producing dubious results, and getting help for things she should have worked out for herself. However, this approach actually suits her learning style and she does eventually learn the essential things she needs to know and understand what is going on. Furthermore, because she has "dived in'' early, by the end of her Ph.D. she has produced several nice papers.

What do you think?
It would be good to hear from beginning graduate students, advanced graduate students, and faculty advisors.
What did you do? What do you wish you had done?