I think the real problem is high volume transactions. In theory, buying money off of localbitcoins assuming you connected to their service anonymously, met with the seller anonymously, etc. should be safe.

But if you're accepting payment and then cashing out, you will need a safe way to cash out and localbitcoins will get you caught fast. Agents would see the money going to a localbitcoins user. They could either setup a sting or just contact whomever has been buying these coins off of you.

Trace btc to the localbitcoin guy, find intersection of his location data from cellphone service company with location data of others around the time of transaction.