Anecdotally, I have observed (myself included) that siblings tend to think that they look less similar to each other than an unrelated observer would say. Is there any experimental data to back this up, or am I completely wrong?
You are not completely wrong but not completely right either. Some siblings tend to think they are less similar to each other, even twins. It may or may not have scientific reason, but it has sociological reason behind it. Every people in our society want to have their own separate identity and they do not want themselves to be compared with others even with their siblings.It might be also due to the result of fact that, siblings pass times with each other so often that they notice distinct differences in both their characteristics and look while ordinary people, looking at them for the first time, can not notice the differences. This is related to the reason why we can not sometime recognize people from any particular race or ethnicity at first look.