Did Vincent Vega shoot Marvin on purpose?

Searching around, I found an interesting detail. When Jules and Vincent are going to Brett's apartment, they open the trunk of the car in order to get the guns, and this is what they say:

             JULES
We should have shotguns for this 
kind of deal.

            VINCENT
How many up there?

             JULES
Three or four.

            VINCENT
Counting our guy?

             JULES
I'm not sure.

            VINCENT
So there could be five guys up there?

             JULES
It's possible.

            VINCENT
We should have fuckin' shotguns.

Vincent says "Counting our guy?", and indeed, they are talking about Marvin. This explains why they don't kill him in the apartment and they take him with them. He's not an hostage, he's an accomplice. This is not a 100% attack-proof evidence, but if he's their guy, it might be that the shot could be indeed an accident.

Furthermore, on the IMDb page about Pulp Fiction, it is stated that:

According to an interview with Phil LaMarr¹, it was he who came up with the idea of his character Marvin being shot in the face. Marvin was originally supposed to be accidentally shot in the throat and survive. Knowing that Marvin would die a slow, painful death, Vincent and Jules decide that Marvin should be shot in the head and put out of his misery. Knowing that this would make the characters unlikeable, LaMarr took his idea to Quentin Tarantino and he agreed to it, figuring that a single-bullet kill would be funnier.

This kind of proves the accident way, since originally he was meant to be accidentally shot, not in a fatal way, and then be killed by the two hitmen in order to avoid a slow and painful death. But here the death is sudden, yet still accidental. I'll add the interview if I find it. If someone finds it, please post it.

^{1: The actor who plays Marvin.}

The only canon reference we have is from Vincent. He tells the wolf "the gun went off, I don't know why".

It is possible he is lying but there seems to be little reason to do so, he is certainly not scared of the wolf and is not shy about sharing his opinions (eg he tells he partner his plan to wonder around having adventures would make him a bum etc).

Overall the only ref we have is Vincent saying several times it was an accident and his generally truthful (even to point of confrontation) nature so I think it was an accident.

I don't have any real evidence, but I was thinking he might have done it on purpose to try and prove to Jules that accidents like that happen - in doing this he is trying to convince Jules that the bullets missing them in the apartment was not a miracle, but just a mistake.

The only 'proof' of this is that Vincent was on the topic of how sometimes 'freak accidents' do happen, and so he may have used that as a way of making Jules think he had done it by accident.

I don't know though, its just a thought.

What I was trying to say, is that he is proving that accidents can happen - this may then trigger a thought in Jules' head such as "Maybe the bullets missing was just a mistake, after all Vincent just accidently shot Marvin". That way Vincent gives Jules the idea without actually arguing with him about it. Like I said, it just my opinion of what went down.