Sure; but nobody who takes the 1000x risk does so believing they don't hold something that reduces that 1000x risk, either, whether deluded in that thinking or not.
My Dad knew the statistics about his chances for success, and he had a very realistic picture (which turned out to be true) of what those statistics would look like when the variable being applied was "him".
But the 1000x risk issue applies in some ways. My Dad was and is successful -- wealthy, retired, married to the same woman since his 20s, spent the latter part of his working life working when he didn't have to, financially. But I'm sure he really would have preferred if it came without a new, dream-ruining, potential problem every other day weeks with sleep replaced with work, being away from home more than home at times, and the myriad of other grief involved. Even though he never let on to us kids, I don't doubt that my Dad probably felt like he was failing for a solid decade, much of which he went without a paycheck, part of which he spent in court filing suit against the former owner of his last business venture (and ended up "winning", which cost him more -- financially[0] -- than had he just ignored it, entirely).
The flip side is that if you really do have something that would reduce that 1000x risk (for your niche product/narrow case/whatever it is that you're doing), explore it, test it, try it. This isn't a "you can't win the lottery if you don't play" sort of things, it's a "you're clearly a smart person or you probably wouldn't understand half of the stuff that's written about on this site, so maybe that idea you think is 'unrealistic' could use a little prodding before you 'bin it'"
Maybe the HN crowd has different problems in this area than the world-at-large, but "an unrealistic expectation of success in business" is not common among grown-ups. Most adults suffer from motivation to simply "learn something new" and their experience (personal and through stories shared by others in our lives/24-Hour News) tell them that most people fail most of the time. If the thing they're trying would benefit them "greatly", that's when the real failin' begins!
Some of the world needn't take the 1000x risk to have a total failure -- life throws that at you on its own and while successes come, too, I tend to focus on the failures. Sometimes they prevent me from taking acceptable risks to achieve something greater. I might have failed at that, but the vast majority of the time, the downside to that failure is just "lost time". Usually the thing I want to make is 100x easier/simpler than things I've done countless times. Doesn't matter, no point, it won't work out. My only hope in those cases is that the thing I'm done has some other benefit, like "at least I'll learn something about this technology if it doesn't work", but I find that focusing on the failure modes is probably the strongest demotivating factor to doing anything, for me.
Conversely, focusing on what (realistically) could result "if this is successful" is a very strong motivator to doing that thing. Granted, the things I'm doing require minimal investment and don't carry with them a risk to loss of life/limb/life-savings, so I can't say that focusing on the success side of things would make much of a difference against those odds, but focusing on the loss of life/limb/savings would result in either "not doing it at all" or "losing said life/limb/savings"
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[0] It was an issue of sale of the business. Nobody but this individual wanted to sell and this individual didn't have the ability to make that choice without the others' involvement but he believed they'd be unwilling to sue him knowing the result would be losing more money than they'd hope to get out of a positive outcome. And if the guy had gotten to know my Dad well enough, he'd not have been surprised when my Dad took the attitude of "let's see who goes broke, first". While Mom wasn't too pleased, I think my Dad actually joked that it was "money well spent" at one point. Mind you, he did this while starting his new business, not collecting a paycheck, and having a very large mortgage on a brand new home in his late 40s, so his opponent's bet that he wouldn't sue was probably a good bet; except that my Dad's humility ended at being stolen from.