We should also keep in mind that all we know about that story was extracted from Smeagol himself, when Gandalf questioned him after captured by Aragorn. This information was bound to have lots of gaps in it. In particular, I much doubt he would have clearly told about the murder of Deagol – perhaps Smeagol (Slinker) first denied having anything to do with it, and then Gollum (Stinker) suddenly came out, evil-exaggeratingly, with the story that Gandalf later told Frodo. Perhaps he actually inferred the whole thing, with some assumptions of his own about the Ring's power. We don't know, in-universe, what actually happened; maybe Deagol's death was more accident than anything else and Smeagol took rather more blame on it than due.

We should also keep in mind that all we know about that story was extracted from Sméagol himself, when Gandalf questioned him after captured by Aragorn. This information was bound to have lots of gaps in it. In particular, I much doubt he would have clearly told about the murder of Déagol — perhaps Sméagol (Slinker) first denied having anything to do with it, and then Gollum (Stinker) suddenly came out, evil-exaggeratingly, with the story that Gandalf later told Frodo. Perhaps he actually inferred the whole thing, with some assumptions of his own about the Ring's power. We don't know, in-universe, what actually happened; maybe Déagol's death was more accident than anything else and Sméagol took rather more blame on it than due.