Earlier quoted context omitted.
The trouble is disproving the null hypothesis. In your test, if one variant beats another, you take that as a weak signal that one may be better than the other. The data doesn't support this. Without applying a standard to your p-value, you cannot disprove the null hypothesis: that your variant is likely no better or worse. I'm not a statistician, but I've run a lot of b-tests.
You're ignoring closed's point that "a priori favors neither group A or B". If you are starting from a neutral position, considering two possible alternatives with neither presumed to be more favourable than the other, then any statistical test based on using one outcome as null and the other as alternative hypothesis is fundamentally inappropriate. Any such test inherently favours one outcome over the other, rather…
The way I see it, you need to prove that A is better than B by a sufficient margin to be distinguishable from pure noise.
So, imagine you put up a landing page with 2 variants. Each one gets 500 visitors. You have a conversion on one, but not the other. It's your suggestion here that there is some significance to that single conversion?
I think the problem is, you have no idea if that user would've converted had she landed on the opposite variant. That is, you can't disprove the idea that your test makes no impact at all.