How does one ask a question about an argument he doesn't even describe? Anyways, here is a link to someone's blog entry regarding the argument, so I will assume the argument you refer to is this, or something like it.
The question is about how decisions affect outcomes. If we treat future outcomes as fixed, then we ought to treat future decisions as fixed, and the that decision will affect that outcome in whichever way it happens to do so. On the other hand, if we consider future outcomes and decisions as variable, then we can see that again outcomes are affected by decisions. We can't treat outcomes as fixed and at the same time, treat decisions as variable (i.e. that there are many options to choose from) and thereby conclude that decisions don't affect outcomes. We have to pick on consistent point of view. We either looking at fixed decisions and outcomes, in which case our claims are material claims about the actual world, and the notion of A affecting B doesn't really make much sense, or we're looking at things as variable, in which case our claims are counterfactual claims about all possible worlds (in "possible world semantics") in which case it makes sense to talk about A affecting B, and we can find that the Idle Argument doesn't validly show that A doesn't affect B.
Note, my remark that it doesn't make sense to talk about A affecting B when we're only looking at claims about the actual world is basically the idea that A -> B is true (where -> is the material conditional) iff ~A v B is true. So for example, the CN Tower is tall, and I am studying, so (the CN Tower is tall) -> (I am studying). Of course, the fact that the CN Tower is tall does not affect whether or not I'm studying. So supposing that "I will survive the jump" is true, it indeed holds that "I don't open my parachute" -> "I will survive the jump" but this doesn't tell us that you could fail to open the chute and still survive. It doesn't tell you how failing to open the chute affects your survival. It just says something about the truth value of the two sentences, and that is all.
The argument linked above has the pattern:
Either A or B.
If A, then C
If B, then C
This is valid structure.
This may be a valid argument, but not a sound argument. The best way to argue an idle argument is to argue the truth of the premises.
The premise could be based on the fact that the person is a heart patient and will die of a heart attack of the fall, regardless of the parachute. Therefore, if the premises are true then the conclusion is true, but it is really a pointless argument and more of a stated fact. If the premises are false, then of course, the argument is not sound.
The only way to attack the arguments validity would be to say it is circular. The premises can only be true if the conclusion is assumed to be true.