So, episode two consist mostly of illustrating various logical fallacies and biases which can make conclusions seem logical when they are not or appear to prove something which they don't and then he finishes off by illustrating what a proper experiment, which will prove a proper hypothesis, should be. One of the fallacies he illustrates is the 'cause-and-effect fallacy' or 'problem of induction' where just if a something is seen to be take place under certain conditions doesn't mean that the conditions caused the outcome, despite seeming logical.

My problem/question is how does Hanks ideal experiment side step this problem?

The only difference I can see between a normal inductive fallacy and Hank's experiment is that Hank's is under controlled conditions and is re-produceable.

Just because something seems to be replicated consistently doesn't mean there is a link. You could flip a coin a million times and have it turn up heads a million times, but that doesn't illustrate that there is a significantly higher chance of the coin turning up heads, it just illustrates what has happened in the past (I believe this problem was illustrated in the video as well, which makes it odd that Hank didn't comment on their being a link). And, surely, therefor, the only real things we can deduce are things which are deduced using logic or direct observations of things causing other things.

So can/does Hank's experiment avoid the problem of induction and actually prove a link between something, or is it simply like the coin toss experiment?