It's probably reference to the indictment, which said that BTC-e was used as a base for laundering the proceeds of e.g. tax return identity theft (something to that effect). That's why the IRS criminal division was involved. I don't think there's any evidence that the exchange itself engaged in identity theft. I imagine the KYC is a way to deter some people from claiming funds. It's shady, but understandable.

I wouldn't want to send them my documents. Not because I think they would necessarily sell them or steal my identity, but because I don't think I want my documents on their servers when they are seized again by the FBI.