Both of these stories start with exchanges telling the authorities what pubkey received their money. The fact that they *know* what pubkey received their money (and can prove it) is a design flaw in monero. Lightning fixes it.

Also, in both of these stories, after the money went from the exchange to the user's pubkey, the analysts watched the blockchain to see where the money moved next, and it went to another exchange with a probabilistic identifier marking the user's pubkey as a possible sender. This enabled them to contact that exchange and find out the user's identity, which led to an arrest in one case and better evidence for the charges in the other.

Lightning fixes this too, because not only does lightning not tell them what channel the money went into in the first place, but when it moves out of the channel, the analysts don't get to see that, because the transaction isn't broadcasted. So they never see the money go to an exchange and thus can never know to contact them to obtain the user's identity.