I agree. Overly smothering a child can lead to it's own set of problems, like codependency, insecurities, and even resentment and embarrassment.

Regarding the peers, it's not so much what the peers themselves think, but how the child sees themselves compared to said peers, and how concerned they might be about what peers may think, say or do. It all boils down to self esteem and the child's own stage of development. At around 10ish, most children begin to pick up heavily on behavioral and emotional differences in their peers. They also begin to compare themselves to their peers as a means of gaging what is normal and accepted behavior. It's all part of child development and psychology.

Another example is accompanying a child to a public restroom. When I was around 7-8 years old, I hated going to a public restroom by myself, and depended on my mother to accompany me into them for use. My own mother had even begin commenting to me that I should be able to go into one by myself, and it was silly to "need" her to accompany me. However, she would oblige me for a while longer, then said I was plenty old enough to go on my own.

There's difference between nurturing and being a helicopter parent. Don't be a helicopter parent. Just don't.