Being MRT certified and part of the Yonex Stringing Team myself, I can tell you that those can only indicate that the store has likely at least one good stringer, but nothing more. Their stringers are more than likely not certified, so one could be a very good stringer (the USRSA certified stringer), but not a very good teacher and as a result, the other stringers could not be as good. Or like in everything, one bad apple might have gone through and the certified stringer may not be competent, let's hope that is not the case.
Unless you had some sort of favor by the organization (which I doubt could happen since it would jeopardize their own credibility), being certified means a great deal. Not all organizations have the same process, so I can't speak for the IART or the ERSA, but to be certified with the USRSA, you have to obtain at least 84% in both the written technical exam and the hands on exam, which are supervised by a certification tester. The hands on exam has many "auto fail" criterias, so you are not allowed to make mistakes. The fail rate of these exams is above 60%. Note that being listed as a stringer on the website does not mean you are certified, it only means that you are a member. I have never met a MRT that was not extremely competent and knowledgeable, but like I said earlier, there could be one bad apple somewhere.
This is my biggest pet peeve when stringing and causes my overall time to be slow, because when I get to the final top 6x crosses I typically end up hard weaving them, and for the problem holes 6+5 (if I remember correctly), you need to pull them through > weave > then pull through last grommet you will get ZERO twisting. I think it depends on the severity of the twisting to actually have a noticeable impact, when I did my first rackets, it twisted like crazy and I never understood why until I did more research, and that particular cross ended up breaking first.