Most people are inherently self-centered and don't tend to think about what other social life you might have. In practice, most are only really concerned about your immediate interactions with them. If someone is overly concerned about your number of friends, they probably aren't worth your time anyway.
I would say that it's difficult in middle and high school because of the relatively compact size of student bodies. However, it becomes easier after K-12, because people can no longer be bothered to "keep track" of others' social lives.
In new situations, the best idea is to introduce yourself to people right away. I've found that unless you introduce yourself right away, it becomes practically impossible to befriend them later. If a new person invites you to something and you actually want to be their friend, you should go for it. No matter how much you don't want to go or how little you end up conversing, it will still portray you in a much more positive light. In my first year at university, I turned down an pub invitation, and it never came again from anyone on that floor!