I'm with Costrin here - what you describe just really doesn't seem to resonate with my experience. Like Costrin, I'm not sure I've ever classified an issue as 'solved', and I'm always willing to hear new information and try to integrate it into my understanding and see the implications on the fly.
Sometimes I may look like what you describe, but I don't think that the mechanics behind it are as you see them. A couple of possible reasons for this come to mind.
First, sometimes I can't come up with a response that I feel is adequate in the moment, though I'm fairly certain that the new information isn't sufficient to overturn my belief. This happens for me more often than it happens for most it seems, precisely because of the precision I desire in anything I say (the "Ps take a long time to come to conclusions because they consider every possibility" thing). When this happens, I'm not usually really satisfied with my response, but I still have to give a response so I say that I'm not convinced, and may give the most incisive critique I can think of in the moment to why the new information isn't sufficient. It's certainly true that my analysis tends to have to do with inner logic, so I can see why it may sound like I'm not willing to reconsider my position, but in reality this confusion is only due to the person I'm hypothetically talking to only seeing the higher-level functions expressed and missing out on the lower-level functions that really are taking the new information into consideration and doing the best (often terribly unsatisfying) business with it that I can in the moment.
The second reason that comes to mind is the one that Costrin mentioned - sometimes I just don't really value what the other person is saying. This is often the case when I don't trust the other person's sources, or when I know that the other person often asserts things without putting them through anything remotely close to the rigor that I put things through before I assert them, or sometimes just due to the other person's tone. (If the other person is being patronizing or speaking with an air of superiority or... whatever else I don't appreciate - I'm likely to more or less ignore their argument and refuse to dignify it with consideration until we've dealt with the problem of their attempt to manipulate the conversational dynamic)
Even in these two cases though, I'm very likely to admit that "I don't know", or to express something as a tentative positions with plenty of modifiers, or to just give a number of ideas rather than asserting any position.
In fairness, I should say that I do see some INTPs (maybe particularly online) who seem to have certain conclusions and stick to them without any willingness to consider, or even be gracious toward, other perspectives. It's really hard for me to speak to those sorts of people though, and I really don't identify with them at all (and not because I haven't thought about whether I might sometimes come off like that).