So it's a kind of doublethink, eh. Shepard doesn't believe the option's real, so he shoots the tube, and the player's OK with it because he wants Destroy anyway.
Convenient. It's a good thing shooting the tube doesn't trigger Synthesis, or you guys would need a different rationale.
That is not what doublethink is, doublethinking is when you recognizing something is the TRUTH, but at the same time ignoring it, twisting it. Shepard was SUSPICIOUS, but he could not confirm whether the Catalyst is tricking him.
I do realize in all options we make a heap of faith, but in destroy, the leap of faith required is the smallest. Shepard does not lose grasp of reality, of reapers' track record, he is playing on the safe side by entrusting less to the reapers and more to other parties. In control, you have to hope the reapers cease to be a threat AND that you could actually control them; in synthesis, you have to hope the reapers cease to be a threat AND that the transformation is seamless, but in destroy, you only have to hope the reapers cease to pose a threat
A different rationale, yes, but not one necessarily helping the Catalyst's credibility.