No, the 20-something-year-old MBA doesn't know. But the 50 year old partner who the MBA works for is likely a world-class expert who has done this a dozen times. And if he's not, he usually knows someone who is that can be brought in to advise - at a price, of course. The partner is usually the one who sold the work and has the trust relationship with the client. So it fucks with the partner's money if the MBA delivers shit work. Management consulting is an apprenticeship business, so the partner is incentivized to make sure the MBA learns how to do things quickly so he can be billed out at higher rates, develop his own relationships with clients, etc. Do that for long enough and you can be a partner pulling in $10 million a year too.
Most big management consulting firms these days also do both management consulting and system integration. The margin on management consulting work is sick, but the projects aren't that big (a few million dollars over a couple months). The margin on implementation projects is much lower, but the projects themselves can be enormous (think hundreds of millions over several years). So you're fucking your implementation guys if you deliver an unimplementable plan. And in a partnership model, if the implementation project fails, the partner who did the management consulting piece of the work still takes a hit.