"All Debts Public and Private" is a strange episode in general, especially when you view it for the first time. It marks a change in tone and pace for the show: more methodic, and a lot darker. This is when Chase starts fully to integrate the "each episode's a mini movie" approach - characters come and go (Artie, for instance, has an entire episode dedicated to him, it seems, then disappears for a few more), and the episodic narrative is more defined and disparate.

Also, information is given to us with no warning or exposition. An example of this is the one you've noted, Veneratio: Barry Haydu, Dickie Moltisanti's "killer". Like many other similar instances, there's no real telling as to whether or not it's true: just clues here and there, for and against, but ultimately unsolved.

I'd say Barry Haydu was not Chris's father's killer. The job is sloppily organised and swiftly done, and it seems too convenient to go through with it so soon after the guy's retirement. Chris's own doubt is confirmed in the whacking scene, and it's there for a reason: it draws our own attention to the sheer wishy-washiness of it all.

Saying that, there's no more rationale in my theory than there would be in one that opposes it.