That kind of is the Big 4 experience and that's not a secret so I am not sure what he thought it would be like unless he took their marketing spin at face value? If he did then that's an important lesson for the future. Otherwise, lots of this sounds like the normal shock of entering the workplace and it is probably helpful for him to keep that in mind. This stage was never going to be easy or as comfortable as the recruitment fairs or internships painted it to be.
If this is audit testing, is there not the previous year's file for him to refer to? Some of the lack of training is likely because they are expecting him to use that as his guide. That's totally normal and workplace training in practice does mean being chucked in at the deep end and being expected to take a decent run at the work and learn by doing. Even in a smaller firm he would still be given a file and expected to use last year's as his reference without hand holding all the way through every task. He doesn't need to fully understand every aspect of what he is doing - nobody does at this stage - he just needs to put his head down and get it done. Treat it like a puzzle.
I don't really understand your explanation of why he thought he couldn't do the testing that he was tasked with. It sounds like he could, he just needed to extend the sample. If so, he would be better to crack on with things rather than meekly waiting for assistance or trying to argue the toss about errors he thinks there are (even though he is saying he doesn't fully understand what he's looking at? That would rile people up). He only has 4 weeks experience and his contribution to the team at this stage is to churn through things.
That doesn't mean it's ok for people to be unpleasant or impolite but it does sound like his expectations are unrealistic and he is putting pressure on himself to be perfect or to understand more than is realistic, as well as being quite sensitive. I also think he is taking the comments about work life balance too literally. If he doesn't hit his client deliverables he will be cut.
He does need to tough it out longer than this. The value of big 4 on his CV will be more about his ability to tough out that environment and build a network, so it will raise concerns in potential employers if he quit so soon.
Parts of training are crap, but as others have said he needs to focus on the end goal rather than getting bogged down in minutiae about a stressed person snapping at him. Keep it in perspective and give it more time. It's not worth packing in a training contract over one crap assignment.
If he was training at a smaller firm, he wouldn't get the extended stretches at college studying and he wouldn't be on a single client for a protracted stretch - college would be broken up into smaller blocks (with people from other firms ) and he would be managing a larger number of client assignments around college. Not necessarily better or worse, but different pressures. My point being that the first year of a training contract is always a steep learning curve and can be a big adjustment, even in more forgiving workplaces than the Big 4.