Anonymously? I don't think so. Most of the payment methods on LBC are Bank/Wire Transfers. I doubt there is any anonymity there when you're literally sending your bank details to the seller/buyer.
Correct. If you're not into meeting up with people to conduct transactions face to face, you're basically agreeing to leaving a digital trail behind the bank or whatever other service can use against you.
What people don't understand is that it in most countries is against the law to act as money transmitter, and IIRC, there have already been articles covering how certain local traders were arrested for selling Bitcoin.
That being said, I too would prefer a wire transfer purchase or sale when dealing with LBC. I am too paranoid to meet up with someone with how Bitcoin is such a wanted asset due to its price. Crypto coiners are walking targets.