I have the following question:

Let's say that you have cited a result from some paper or textbook. What is the probability that you have carefully read through the relevant section or chapter?

I don't intend to be flippant or rude, but it seems very unlikely that everyone reads through everything that they have cited. Rather, if one wants to use a theorem that is not in a standard textbook, one typically finds another paper which cites the desired result and steals that citation, thereby passing the responsibility of ensuring correctness to someone else. This saves a lot of time, but seems to propagate inaccurate citations and poor understanding of the work being cited.