This is my experience as well.
When done slowly, a wider stance does make it easier to keep your balance. When done fast, however, the risk of uke falling on the knee seems to me to be much more of a concern.
If you can't keep your balance with a stance narrow enough to be safe, the solution is probably to practice until you can, not to adjust your stance to compensate.
The training I got at the original Bond Street Dojo seems to have been significantly different than either alternative mentioned thus far in this thread.
1. Feet together in a "T" with the heel of the "non-load" foot at the arch of the "load" foot beneath the hip over which uke will rotate.
2. Always remove the bearing leg and hip while releasing uke, precisely to avoid the risk of uke falling on the knee.
In part, this reflects the significant influence Kuroiwa Sensei had on training at BSD; senior instructor Christine Jordan was relentless and adamant about the removal of the leg as a safety measure and I've followed her lead in that. A number of years back, I had one particularly otherwise exemplary student who didn't listen to my admonitions on this point for a period of six months. Then he damaged his knee, needed ACL surgery, and effectively ended his training. Since then, I've become more insistent about the need to remove the leg.