This is definitely a better way of putting it.
As an aside, when I began at the current church in which I serve, I read the constitution written by a previous pastor. He made a similar mistake in his wording. He worded it thus: "______ Baptist Church is a member of the American Baptist Church."
Aside from the fact that there is no such entity, the church did not belong to any association or convention that remotely resembled that name. When I asked him what his intended meaning was, he simply said, "we are part of the Baptist Church... you know... the universal one in America."
arrrrrgh
I simply said to him "you may wish to bone up on your ecclesiology."
I think he probably meant that ____ Baptist church is part of the family of Baptist churches in America, or a church which holds to the practices and beliefs commonly called “Baptist” in America.