[RPG] Can conflicting descriptions of the recent past be handled better than GM fiat

I've been having a problem in RPGs lately where participants, myself included, have radically different ideas about what just happened on a basic factual level. For example, in a recent Pokémon RPG where I am a player, a significant conversation was had amongst the players and an NPC about whether or not to tell Will's Alakazam we can talk to Pokémon. In the course of the conversation, from my perspective, one of the PCs asked a question of the group and the NPC responded first. However, another player was convinced that the question was asked and then my PC and another PC responded, and only then the NPC responded. I will use this example throughout this question as an illustration, but please keep in mind that it is only one example of this sort of problem and that specific case has already been resolved; you can feel free to use it similarly to illustrate the advice you give in an answer, but the actual specifics of that advice as applied to this situation are not important to me.

These sorts of disagreements about basic facts can be a serious problem when players end up making plans that rely on fundamentally incompatible versions of the world, and lead to lengthy arguments and discussions. Although this hadn't come up much before until about a year or two ago, it's been coming up a lot since that time, particularly since the first steps I outline below consistently do not ever work with several of our newer players.

The current system that we use for this has developed in an ad hoc manner and is not particularly thought out. It goes like this:

1. There is a disagreement. In this case it's about whether or not the PC in question insulted the NPC by shutting them down for interrupting when no one else was talking.
2. We clarify whether the disagreement is about material or immaterial facts (i.e. whether we are disagreeing about what happened or what that means. This isn't always obvious– "John murdered Sue" is probably immaterial if the issue at hand is whether the killing was justified rather than whether the knife propelled by his hand entered her heart. The important part is to isolate what we disagree about and determine whether or not it is something that we think should be obviously true or false to both characters regardless of their value differences). In this case what order people spoke in is a material fact, and no immaterial facts are disputed– we agree that if the PC in question had shut the NPC down in that manner it would be insulting, but we disagree as to whether or not that, in fact, happened (i.e. whether or not other people were currently talking at the time).
3. If the disagreement is about immaterial facts, it's not relevant to this question, but it enters a separate process
4. If it's about material facts we survey the group. Generally, in the past, people change their minds or at least acquiesce to our carrying on with things being the other way if everyone but them remembers something differently. For two people we now play with in several games this is never the case. In this case, everyone but the player of the PC who shut down the NPC (myself, another player, and the GM) agrees that no other players had indicated their PCs were talking at that point. The player dissenting continues to insist that we had, in fact, done so, though.
5. If the group cannot reach consensus in a timely fashion (<2 hours), the GM issues a fiat or declares that discussion between the invested parties will happen elsewhere as the rest of us keep playing. Those side conversations usually take 2-4 hours when I am a party and 4-6 hours otherwise. In this case, the GM declares by fiat that there was a miscommunication in the in-character conversation, the NPC is not insulted because they thought what was happening was the same as what the PC in question thought was happening, but generally everybody is momentarily off-put or confused and then things are worked out off-screen and the PCs are getting along again and the main thrust of the conversation can resume. It takes only 30 minutes before that fiat is given (this is unusually short) and then another half-hour or so to discuss/explain what the fiat means.
6. If GM fiat was issued, although the disagreement is officially resolved, there are still always inevitably problems of late, unless the GM fiat is in line with the position espoused by the new players, if either player is in the game (they are never both in the same game, so far). These problems take the form of more disagreements about what's happening, material or immaterial, in all areas related to the fiated thing, which inevitably morph into rehashing the same disagreements that were had before just with putatively a new issue at hand. Frequently the content of the last GM fiat is also a matter of material disagreement in these cases. This starts the process over, usually resulting in another GM fiat after a couple of hours. In this case the fiat was sufficiently concillatory and no further problems around that particular issue arose. The fact that we quickly ended up is a 4 hour conversation about a different conflict between the GM and the player in question related to a different past fiat from a previous session may have had something to do with that, however.

This process is exhausting and frustrating for everyone involved. Is there a better way to resolve these disagreements about basic facts?