Honestly, I think calling quoting as well as linking EVElopedia-Articles "citing player resources simply to win arguments" is pretty close to saying that people doing so are "doingitrong".
Why do I think so?
First, the implication that people use EVElopedia articles "simply to win arguments" means that those players are somehow more interested in 'winning arguments' that 'roleplay'. I'd respond to that, that 'winning arguments' might very well be part of roleplay and honestly I don't see how trying to win an arguments is generally such a bad thing. Also, I don't think that by quoting EVElopedia, everyone means to simply 'win the argument'. If I RP in EVE I don't want to debate with others if the Empire exists or not. There are established facts, they are - whether people like it or not - established by PF and thus in part by EVElopedia, being one of - if not the prime source for, e.g., the history of the factions , their demographics as well as their constitutions. Citing EVElopedia is thus, for me, a way to get a debate back on track.
EVElopedia leaves plenty of space for debates and discussions. I as a player don't feel like debating anything that some player made up for himself and that is in contradiction or stark contrast to PF, nor have my characters time to do so. Still, Wikipedia rarely states that "this was good for x" or "that was bad for x" or things like "the Gallente can't say it was a war of Caldari aggression". Rather than doing so, it gives such debates richness as it provides actual background to it. By the way, the Amarr didn't eradicate half the Ni-Kunni population - and quite honestly, I don't see why there would be a need to people claiming that: One can wonderfully debate on the benefits and downsides to the Ni-Kunni having been reclaimed along the lines of PF.
I think it's just outright wrong to say that quoting EVELopedia makes IC conflict impossible. The only thing is that you need to put some effort into getting to know what you debate about. Sources in general and that is also true for EVElopedia mean that you can't debate a topic simply "out of your ass". Some people might feel that this is hampering their RP. I think it leads to a more immersive, realistic world and more engaging and interesting debates.
And no, I don't simply trust that fact will prevail, I'm sorry for that I'm by far too much bitter vet: It makes sense to give a link to the facts as many people, even RPers, don't read all the PF available. I did only skim the extensive body of PF available about the Federation and the Caldari and the better part of the Republic.
We had people coming up with all sorts of claims about the Amarrian religion that were more appropriate for a debate about Abrahamic religions, which were quite popular among non-Amarrians, even though they stand in stark contrast to the PF we have about the Amarrian religion.
As the community was quite split on this matter I don't put much trust into it, no. Honestly, I think it's quite stifling for Amarr RP that people rather debate Abrahamic religion than Amarrian and yes, I think that pushing that onto the Amarrians is on par with claiming to be the only child of Otro Gariushi. In my experience if someone is opposed to another faction there is a good chance that they will rather jump on the bandwagon that is rolling against said faction, than first to check whether it holds up in regard to PF. People just don't mind what the PF is. That's not to say that their characters shouldn't cheer in support for every straw-man put out there. But yes, in that case their characters make the impression of being uneducated at least and stupid at worst. Or should, at least. If no one is noticing it because everyone is ignoring the PF then I'm feeling like I can't enjoy this game with this PF and a community that doesn't care. Thus, I just throw in some linkies every now and then. I also enjoy the provided links by people who specialize in other parts of PF. After reading it, I'm still free to portray my char as being as ignorant as I like or to come up with sophisticated points to engage the topic - or to not engage at all.
The claim that "Playing judge concerning the legitimacy of other player's roleplay starts with Jamyl's love child and ends with local police have no jurisdiction over us, you're just making it up!" is a slippery slope indeed: In the sense of being a classical fallacy. Is there a necessity that judgement on the claim that someone is Jamyl's love child will lead to judging every tinsy pinsy bit of RP? I really don't think so. Sure, not allowing any freedom in RP is wrong. Similarly allowing every freedom in RP is wrong, there are established facts in EVE, there is a PF and people should stick to it. Therefore, the solution isn't in never ruling something out nor in always ruling something out, but in ruling out what is worthy to be ruled out (PF gives a good idea of that) and not to rule out what doesn't need to be ruled out.
Thus providing ICly a link to PF (that is that which we all should adhere to anyway) can't be that bad, imho.
As to the second point that EVElopedia is a 'player resource'. I agree that it is, but I don't see that 'player resource' means 'OOC'. In my opinion a 'player resource' can be OOC as well as IC. There are several good reasons to look at certain parts of EVElopedia as accessible to our characters, among those that things like the general history of a faction should be, reasonably, be accessible in an encyclopedic article and that's a thing the EVElopedia provides.