I don't know the VW, but my BMW manual describes the function pretty well. It explains also that an automatic call will be initiated on certain events, but it also says that if a call was initiated, keep on talking even if the sound on your side is bad quality, they might hear you even if you don't hear them. Also, even if you can't speak, the rescue will be sent out since they receive the position information from the car, assuming the GSM reception is fine. Regarding the differences between your own call and the automatic call, the sound problems could have been caused by a speaker damage, or by the simple fact that each call is unique, so a different connection might result in a totally different sound quality.
I am sure that your conclusion is incorrect regarding that the system is useless. It is highly probable that they would have sent out a rescue team at a higher alert level if they wouldn't have been able to talk to you at all, because in that case they have no real idea of the situation, how serious it is, how many involved, how many injured, how serious injuries and so on. By default, they take these automatic very seriously. Of course, if they can hear you and you say that no one was hurt then they might lower the alert level, but that's up to their judgement of the conversation. I am pretty sure that the system is NOT useless, not even in your case.
But it's good that the air bags were not deployed and no one was hurt.
