The crucial question is: did Wakefield cause the drop in vaccination, or was his popularity a symptom of some underlying cause?
A single observation is not enough even to establish correlation. The only way you could build a case is with Bayesian statistics. Bayesian statistics (as opposed to frequentist statistics as used in clinical trials) is really a calculus of belief, saying "If you used to believe the state of nature was X, and you observed Y, then you should now believe X'". The answers depend massively on what exactly X is, and what you believe the relationship is between the state of nature and the observation.
In the cot death case, or in DNA testing, there is a fair amount of measurement to tell us what a sensible prior belief is, and how to change it in the light of evidence. But there aren't enough parallels to the Wakefield case to be at all certain.