Uh oh!! I gotta go talk to them.
In all seriousness, check your surgical report (or if you gave it to them, just ask) to see what your c-section suture material was made of. It will say something like 0 Chromic or 1 Vicryl, etc. If it's chromic, you may have a slightly higher risk but it means you need to avoid induction or pitocin use as much as possible (which shouldn't be an issue with them anyway). If you have vicryl, then there is absolutely no reason to believe that your risk is in anyway elevated vs a double layer suture. And you can tell them crazy VBAC Dana said that.
Their old back up doctor used to require single layer suture VBACs to have an IV in. During my visit with him, I went over the studies and explained why I disagreed with calling me a higher risk. I told P&L I was going to do that ahead of time so when I was talking to him, Louise walked in with my chart and winked at me on her way out. He was really nice about it though and didn't say anything about an IV so I just had a saline lock in place. After my big conversation, he still quoted my risk as 1%.
Bottom line is that you don't even need to worry anyway. They are super patient and if they have any concerns about an increase risk of UR with a single layer suture, you won't see it in them during your labor. I know of at least 3 women who VBACed with them on single layer sutures. My labor kept stalling so I used nipple stim to keep the contractions going. One of my friends (who is on here as well) opted to use a little pitocin since her water had been broken well beyond 24 hours and they kept it a very low dose (as opposed to many providers who will increase the pit dose every 20 minutes).