Every family and every child has different means and needs and you need to balance out your own. It does indeed bring out strong feelings when you believe another child is getting an advantage you cannot afford to provide for your own child. Maybe you were not in "the loop" because your friends were being sensitive to that fact, but, really, you don't have a role in those decisions for other families so I guess I do not understand the whole "loop" concept unless you are just talking about being informed, which you are!
You can be your own child's advantage. Spend more time providing the extras - library books, reading time, art "lessons," sing-alongs, field trips to the zoo or the museum or the aquarium - and less time worrying about what other families may have that you do not. A lot of the extras private school provide impart a layer of cultural "polish" to their students public schools cannot afford, but you can accomplish a lot of that by simply following some of the steps above. (I have had kids in both settings.)
Most private schools have reading lists online. Check out the books they recommend for your child's age group and head to the library! Make it fun. When another child says, "We read that book at my school," and your child says, "My Mom (or Dad) and I sat out on the porch and read that one this summer," guess which kid will be the jealous one!