To be honest though I don't find it surprising that factor analysis would find high correlations between some traits. Actually, this is really concerning if that's the basis of the whole thing. You can find correlations anytime you look for them. How were these correlations validated? I mean- how do we know that the big-5 don't just model noise in the analysed datasets?
I don't know the details of the approach (though someday I would love to study them) but I gather that the correlations are very strong and that it has been replicated many times (including in different languages). Though what is key is that the correlations are weak between groups of traits. You can find large question banks they've used too. I think that even using disjoint sets of attributes/questions you will still get the same groupings.
EDIT: To add just a bit more, of all the replication scandals in psychology today, the Big Five is one of the few frameworks that has withheld the storm.
To be honest though I don't find it surprising that factor analysis would find high correlations between some traits. Actually, this is really concerning if that's the basis of the whole thing. You can find correlations anytime you look for them. How were these correlations validated? I mean- how do we know that the big-5 don't just model noise in the analysed datasets?