AITA for starting my wedding on time and not waiting for my parents?

I got married on Saturday, and it was absolutely amazing except for one thing: my parents showed up late. They knew the ceremony time, and my husband and I made it very clear to everyone, both in the invites and in person, that we were going to start exactly at that time. The venue cost us a lot of money (we paid for the entire wedding ourselves) and we were only able to use it for a limited amount of time, so we wanted to make every minute count.

So the wedding day came, and half an hour before we were scheduled to start, my parents still hadn't showed up. My husband and I both called them multiple times but nobody answered. We waited and waited, and still heard nothing. Finally, the start time arrived and my parents still weren't there. I was really pissed off at this point. The wedding coordinator asked if I wanted to go ahead and start the wedding, and I said yes. All of our other guests were already there, and we wanted to be considerate of their time.

My parents showed up 15 minutes later and missed the entire ceremony. It turns out they did leave early but got rear-ended at a traffic light and had to deal with insurance, police, etc. They only have a landline, no cellphones, so they couldn't get in touch with me. Obviously there's no way I could have known this.

I'm still frustrated with them for not making more of an effort to get to the venue early, and they're furious at me for not delaying the wedding 15 minutes so they could be there. AITA?