Couldn't agree more. My first step when troubleshooting anything for someone else is to extract as much information as possible to understand what I'm dealing with. Having that information from the start would save me a lot of time.
>I can't say I perceive the dismissal from the quote alone.
True, the quote alone is not necessarily dismissive or arrogant, and your interpretation could very well be correct. I'm assuming it was dismissive because the author seems troubled by his own response, which he interprets as "I just told him that he's wrong and he doesn't know what he's doing". That's where my interpretation comes from.
A bit off-topic but I've actually got an inverse problem... Before contacting support I'm trying to collect as much diagnostics as possible, so my first message tends to be a long detailed list of what's the problem, what I did, and what possibly useful (to best of my awareness) supplementary diagnostics I've already performed. This frequently confuses first-tier support folks who're used to people reaching out with mere "nothing works pls help!!1one" and going through checklists.
I've also had humbling experiences, particularly one with me going through what I thought was relevant and a very nice tech support lady telling me the equivalent of "but did you make sure you turned it on?", and she was right.
Overloading tier-1 techs with too much information rarely does any good, from my experience.
One problem is that most people are socialized heavily against going into these kinds of details in almost every situation they will experience. Only engineers are frequently around other people who want to know specifically what "it doesn't work" means. And even in those cases, you've got to tailor your level of detail with care. It's no wonder people learned to just say "it doesn't work", in the same way that they learned to reply to "how are you" with something vague rather than something extremely specific.
Also, I can't say I perceive the dismissal from the quote alone. Those two short sentences feel like a very brief excerpt from beginning of a conversation so it's hard to gauge, but I feel that it's an exclamation of surprise that's non-committal and lacking an explicit offer to proceed with details, rather than dismissive (or worse). Circumstances, tone, body language, relationship and other things may make it vary, of course. Can't say it's arrogant either, "no way, it must work" is a legit exclamation that doesn't imply incompetence (unless, again, tone etc).
I'd say it's just passive, not taking any initiative to troubleshoot and communicating just the assurance that the problem must be solvable, then bouncing back to the inquirer. In my understanding, it's more of a lazy/not being in the mood, not dismissive (and I'd have a really hard time trying to call it "toxic").