Both P.Lee and Don Jefe are correct.
What I would add is that sourcing and manufacturing in other countries allows companies to maintain a certain level of ignorance, or at least 'plausible deniability', providing them with the savings of third-world standards without having to actually get their hands dirty.
This was seen very clearly in the recent Rana Plaza factory collapse in Bangladesh.
What was happening in the clothing industry was (and is!) that western companies were outsourcing at least part of their production to India/Pakistan/Bangladesh but doing so through middle-men, who then farmed to work out to various factories.
In one 'supply chain' reported on, the brand contracted their work to a middle-man company in India. That company then subcontracted the work out to a factory in India who only did a portion of the work themselves. The bulk of the work was farmed out to several factories in Bangladesh. Even then, there were instances where, due to workload or extra orders, some of the Bangladeshi factories further subcontracted out to other, smaller firms.
It's a mess and, as each part of the chain must make a profit, the end result is that the people actually making the product are paid a pittance and are working in, well, death traps.
All through that, however, the furthest the original company sees is the factory in India, which is a nice, clean and relatively modern affair. Unfortunately, nearly none of the work is actually done there.
So, as Don says, there is always the potential that the complication inherent in global supply chains will result in these situations, but there is also the simple fact that some companies prefer this complication for exactly that reason - they end up getting the benefit of the questionable practices (lower costs) but don't have to actually engage in those practices themselves.
In other words, it's not so much that they can't know but that they don't want to.