Correct, implying that the ICAO ratings are an indication of a specific carrier's safety is misleading. They mostly refer to the specific country in which the carrier operate and the oversight that they exert on the airlines. The rating in Qatar appears to be mostly influenced by some lack of transparency and unwillingness to adhere to certain standards, but this doesn't automatically imply that safety is compromised in any way or form (for all we know, there may be even more stringent albeit different standards). This is a very serious topic where I think speculation is inappropriate - better leave that to the Krug.


Back on the main topic... My two cents:
- I find the Skytrax rankings and system laughable (not sure why people, particularly frequent flyers, get so worked up when others note how irrelevant that thing is)
- Nevertheless, I do find QR a "five star" airline. Taking everything into consideration, it's an excellent way to fly. Would I fly them when I have a direct option, or when I do not have to be in Doha? No, I prefer convenience. - Are they among the very best airlines in the world? Definitely yes.
- On the point raised by the OP, many airlines don't offer a 24h call centre accessible by any and all countries. British Airways don't even offer that in their home country (unless you are GGL). Overall, I don't think is an indication of the quality of the airline.