Gelman has been pretty adamant about the idea there probably always is some real correlation between almost any two measurements (that is why he advocates his t

Gelman has been pretty adamant about the idea there probably always is some real correlation between almost any two measurements (that is why he advocates his type M and type S error concepts). Perhaps you are confusing "skeptical the parameter is far from zero" with "skeptical the parameter is non-zero". It makes a big difference.