From the book: Mattis wanted Theranos devices on the field, informing treatment of troops in realtime. This was routed to the Army's office of regulatory compliance. The compliance officer raised ethical concerns about Theranos' regulatory strategy, which he shared with the FDA. The FDA also found the strategy concerning. Mattis knew this. Instead of prompting him to take a closer look at the company, it prompted him to summon the Army officer and make him explain himself.
The upshot of that meeting was that Mattis agreed that Theranos devices didn't meet regulations necessary to actually be used on troops in the field. Instead, it was proposed that Theranos do a more limited trial, using anonymized blood samples. While this wouldn't save lives, it would at least prove Theranos' capability to do accurate blood tests on small samples. Theranos didn't have this capability, and never followed through with the trial.
Even though Mattis supposedly wanted this tech in the field with his troops, he apparently did not notice that the company whose board he joined never actually made any real attempt to get there.
And it's not so much about what Mattis knew and when. It's about the fiduciary responsibility of a board of directors to direct the company. There were things he should have known, but didn't. Like the fact that Theranos never actually did any kind of calibrating study, where their results were compared to known-good results. The revenue projections they were showing the board were based on partnership contracts that were never produced when requested by board members. Etc.
There's a lot of basic stuff that Theranos was doing wrong, that should have been noticeable to anyone who asked even simple questions. Just the failure to produce definitive documents when requested by board members should have been enough. Assuming Mattis were actually interested in that.