It was mentioned it was like a copycat because the killing method was different. This was because of Alex’s different state of emotion. His murder was more because of Clark loving the doc not because the doc loves Alex. The murder was done to provocate Clark. Clark got Alex’s messsage and Alex gets really happy saying that Clark truly understands him. His files are history of victims he investigated (because he likes seeing others in misfortune) not his murder victims. It doesn’t make sense storywise if Clark killed the doctor. His quirk always is that he enjoys stories of people dying but doesn’t kill them himself. The fact that he killed Alex shows how much he cared for the doc. If Clark killed the doc he has no reason to kill Alex.
I don’t know where people got the idea Clark killed the doc. Alex killed him. That should be clear by now. Clark only has the finger because he found it in Alex’s house. It is one of the first things he ask for once he gets kidnapped by Alex.