appeal to authority vs. halachic reasoning - a practical question

Let me give the general platitudes of the previous post some practical flesh and bones as it relates to current events, at the risk becoming a lightning rod for criticism. If R’ Chaim Kanievsky shli”ta indeed said (I do not trust second hand reports) that flying on an airliner which had previously engaged in Chilul Shabbos poses a risk of sakanas nefashos, a Pandora’s box of questions has been opened. As advice, such a statement transcends rational explanation. In terms of an issur of placing oneself b’makom sakanah, such a statement certainly demands explanation. Can I ride in a taxi if the driver is a machelel Shabbos, or is this sakanah as well? Why do the dinim of chilul Shabbos have to do with issues of sakanah? Is this a special din that relates to Shabbos, or does it apply to any enterprise run by ba’alei aveira? And most importantly, what are the sources that would support such a statement, whether construed narrowly or broadly? As far as I know, no one has suggested answers to these questions, but even more troubling, no one seems to think these questions need to be asked.
Is it any wonder that such propositions sound bizarre to unaffiliated Jews who are led to dismiss Orthodoxy as a “cult of personality”? Aside from an appeal to the authority of R’ Chaim, is there any reason to accept such advice or a psak halacha sans evidence, sources, or proof? If the Noda b’Yehudah felt unqualified to dispense Torah without sources in shas and poskim, are 21th century talmidei chachamim not to be held to the same standards?
I am not questioning R’ Chaim Kanievsky’s Torah wisdom one iota. Afilu sichas chulin shel talmidei chachamim tzericha talmud is precisely what causes me to wonder why the tools of critical analysis and debate using sources, proof, and reasoning have suddenly been abandoned in favor of blind obedience to authoritarian wisdom. Why is this an exception to the process of talmud Torah?