That’s half of the meaning, but a half-truth is an unbalanced thing and it misleading by its very nature. You have ignored or misunderstood what an “establishment” of religion is all about in historical context.
Establishment of a religion - means that the govt makes one or more religions the official religion.
The USA never had an official religion -(though some States/Commonwealths did for many years)
and lets not forget an important part of the 1st amendment "or prohibiting the free exercise thereof"