Humans applying observable correlations are indeed how biased decisions get made, mostly because humans are very bad at choosing which correlations to pay attention to, and at weighting them appropriately.
That doesn't mean that just because algorithms based on big data will tend to apply those correlations correctly, that the result will be desireable.
The reason you can't ask people directly about their age, whether they have kids, are married, etc. has nothing
to do with whether the correlation between those factors and undesireable-to-employers traits (example: single mothers typically needing more schedule flexibility to take care of kids and using sick days as a result) is statistically valid, and everything to do with the fact that filtering people out from employment opportunities based on those factors is just wrong
Using Big Data powered algorithms to find better and narrower proxies for those traits (so that you're now discriminating against 'people who are likely to use sick-days when they aren't actually themselves sick' regardless
of whether they happen to be single mothers), though legally defensible, doesn't seem to be a huge improvement to me.
Just because we can figure out more efficient ways to discriminate than this: http://www.hrworld.com/features/30-interview-questions-111507/
doesn't mean we should.