  Well... Let me be the first to say that Bad Religion is a pretty good band... But to say that they essentially started punk is going to far.
It is impossible to say that any one band really invented any genre of music. The reason for this is because there is always someone else who did the same thing earlier. All this later band did was change it and in the case of punk, just took rock and put in some anti-gov/anti-whatever lyrics. The lyrics part may be too general, but you know what punk bands sing about. A great example of the altering of music is Bob Dylan. He is a great song write in his own time but there were people before him. People such as Woody Guthrie. Obviously Dylan didn't invent the folk-singer genre, he just took it and modernized it. Much like this, Bad Religion just took the punk genre, and made it more punk. It didn't make punk, it made their own punk. Every good band has their own little niche in their genre. Whether it is through a unique voice (Johnny Cash) or through their playing style (Jimi Hendrix).
Because of all this, it is hard to say when any genre really started. Take rock-n-roll. RnR was essentially formed in the 50's by a number of bands. The fact is though, those bands got many of their ideas from earlier music (Jazz, swing). Now I leave you with a song recommendation... A Boy Named Sue by Johnny Cash. 
