No, no, no. You're trying to triangulate to a corner of the world where your fundamental assertions are still unchallenged, but you can't get there. Here's the problem:

The assumption of the experimenter is that test subjects should assume the tape-recorded messages are factual.

Not in evidence, not tested for, not relevant to the discussion. The assumptions of the subjects is not under investigation, nor does it have any bearing on the outcome. The only question is whether the subjects want to hear the information or not - its veracity does not enter into the discussion. The experiment was published in August 1967. Cigarette packs had only had warnings on them since 1966 - even then, they were pretty ambivalent ("Caution: Cigarette Smoking May be Hazardous to Your Health"). In 1965, 42% of adults smoked. It's entirely possible that the experiment was conducted before even that mealy-mouthed warning made it onto packs.

So you can't just invalidate the experiment by presuming the experimenter presumes the subjects are taking the recordings as gospel truth. It isn't part of the experiment, there's no basis to make the assumption, and the facts on the ground indicate that it's a silly assumption to make in the first place.

The only thing being tested is openness to information based on the content of that information.