I disagree. In the least convenient world where the STD test imposes no costs on Alex, he would still be instrumentally rational to not take it. This is because Alex knows the plausibility of his claims that he does not have an STD will be sabotaged if the test comes out positive, because he is not a perfect liar.

In a world were STD tests cost absolutely nothing, including time, effort, thought, there would be no excuse to not have taken a test and I do not see a method for generating plausible deniability by not knowing.

Some situation at a college where they'll give you a cookie if you take an STD test seems quite likely

You situation does not really count as no cost though. In a world in which you must spend effort to avoid getting a STD test it seems unlikely that plausible deniability can be generated in the first place.

You are correct "Avoiding the evidence would be irrational." does seem to be incorrect in general and I generalized too strongly from the example I was working on.

Though this does not seem to answer my original question. Is there a by definition conflict between "Whatever can be destroyed by the truth, should be." and generating plausible deniability. The answer I still come up with is no conflict. Some truths should be destroyed before others and this allows for some plausible deniability for untruths low in priority.