You certainly do when placebo effects are involved. Also, even without placebo effects, is what you said true when taking into account anthropic reference classes? Finally, if we don't know the cause of the Fermi paradox, we can not be sure that flooding the galaxy with radio signals won't causally effect the chances of our escaping the paradox so the analogy here might be to updating on the chance of your getting sick because you got yourself vaccinated.

Still, I like how you put your objection and it's one I should more thoroughly address if I work further on the idea.

I read the logic as something like Timeless Decision Theory. If you reached this conclusion and planted this evidence, there is a reasonable chance that previous actors in similar situations did so as well, and given enough previous actors, you should see the results. Since you don't see those results, either there haven't actually been very many previous actors, or something else about your assumptions is invalid. In either case, the logical basis of the Great Filter conclusion has been drastically weakened.