NoeL has changed my mind, which I haven't expressed prior to this post. Very great insight! But to be fair, I hadn't put much thought into this initially.
Most of us probably want to be correctly understood in most situations. Therefore, most of us want our intentions to be understood too, with the intention being that people simply understand what we are trying to say, be it a fact or an opinion. That requires one to reflect on that reception before the words come out, thus we try, if we can, to choose the words that we think will make our thoughts correctly understood. As a professor, I have had a lot of experience at trying to do that, teaching the same material many times over. I had often asked myself: How can I present this better? So one who does that naturally would put reception first, in order for it to correctly interpret the intent of sharing our knowledge.
On a different note, that is not to say that one needs to be politically correct, when it comes to talking about more political or sensitive matters. I find political correctness to be prioritizing reception first, but with an intent that differs from simply being understood correctly. It's no longer necessarily about wanting to be understood on your actual opinions correctly, but rather to say something in a way that gives you as many cheers as possible, and as few jeers as possible, at least among a certain group of people that you are trying to please. You don't have to be honest or properly understood on your intent in order to achieve that goal. If it's for the sake of looking virtuous among your peers or a certain social group, the intent is more geared toward being liked, rather than what you might actually believe about a subject matter.
But either way, this still prioritizes reception over intent, because reception must be reflected on first, and thus adjusting how you carry out your intent. They often work together, but one is dependent on the other when thinking about it thoroughly, assuming that one does and one cares.