I always ride an 8-9 din (mostly because my feet are tiny), and for whatever reason I have found a difference in retention between bindings that only go to 11 versus bindings that go to 13 or 14. Even with well reputed bindings. For example I had some look pivot 11's and some look pivot 14's and I had to stop riding the 11's because I kept pre-releasing even at the same din setting on both, but I had no issues with the 14's. I have tyrolia attack 13's that work just fine set to 8.5, but I've never tried the 11's, and I've never had any issues with marker griffon 13's. I also had issues with STH 13's but not STH 16's. So yeah in theory it shouldn't matter, but in practice it does seem to matter. Not to the point where I need to get 18 din binding, but enough that I avoid bindings that only go to 11.
There are a lot of factors to consider here though, if you have a small foot the bindings will have trouble keeping a hold of it. If you ride a stiffer tight fitting boot you'll be able to more easily leverage extra force into the binding. Longer heavier skis will also need a bit more retention in my experience. And then of course your own weight and strength. It could be you'll be fine with an 11 din binding, especially since you normally ride a 6.5, but there definitely is a difference in retention versus higher din bindings.