The channel peer you open the channel with knows both the history of the UTXO used to open the channel, and every subsequent transaction routed through them. If that UTXO was split from another that's later identified to you, then the whole channel is identified to you and thus anything routed through your channel peer is attributed to you. Then with timing analysis, later hops can be linked to the origin channel thus the whole chain can be broken.
If I'm incorrect please inform me this is the limit of my knowledge.
