Would stitches have been better for facial cut?

My daughter got a cut on her forehead from running into a sharp metal corner on a piece of furniture. I took her to a doctor and she said it should have one stitch, but they didn't do that kind of thing there. I took her to the hospital and three different people said she didn't need one. It is less than 5mm long but is kind of deep. They said it didn't need a stitch because it didn't go through a certain layer of skin, I forgot which. They put on a steri strip with some adhesive. I am reading through this information I have found and it makes me think she should have gotten the stitch. Which would be best for preventing a scar for her particular injury? Considering it is kind of small, will the steri strip hold it together for minimal scarring? The thing I am worrying about is the depth, and this information I am finding that facial cuts should be stitched. But it isn't that long so maybe it is an exception for facial cuts that don't need to be stitched. I would have done the stitch if I knew it was better. It looked like more than a superficial depth to me.