Toritoribe-san is not saying they are completely and entirely interchangeable in all contexts. Please read what he's saying again. He's specifically saying that despite the fact that the verb itself is volitional, the speaker does not have complete control of the action. This is different from your examples where they are both explicitly controllable actions on the part of the native speaker.
That said, I think there may be a slight bit of overlap, but I'm not exactly sure why you're unable to parse this ように in the same way as the "so as to/in such a way as to" meaning like それと向き合う形になるように in your other topic. It's not specifically saying "in order to", but rather describing an action performed in such a way as to elicit a certain result that the speaker does not have complete control of, but is hoping that the action will lead to or elicit the desired result.
I've expressed this before to you, but sometimes I think you're reaching a bit too hard to find an explicit black-or-white rule for every simple grammar point. I realize that this is a bit "meta" and perhaps not the clear, 100% "this is right and this is wrong" answer that you're looking for, but I would suggest that when you see a certain phrasing used in native materials, and a native speaker like Toritoribe-san tells you that it's completely natural, that you don't try to fight that and think "but this doesn't obey my interpretation of the textbook rule", but rather try to find a way to mentally adapt the prescriptive definition(s) you may have seen to allow for the slightly different usage or example that you have seen in practice.
It's not really purposeful to take an expression written by a native speaker, and about which another native speaker has said "this is completely natural" and think, "but according to my textbook it shouldn't be!" In that case, it's probably not that the textbook or native speaker(s) are wrong, but that your current interpretation is simply as-of-yet too narrow to account for real-life usages that you're only now just encountering. I'm not saying this to criticize you or to be mean, but simply that you should use these opportunities to let your understanding of things deepen and expand, rather than fight against them because they don't jibe with what you already think you know.