I don’t think that’s nitpicking at all. The term “church” as we understand it today isn’t even found in the New Testament. The word used in the New Testament is “assembly” and the corrupted interpretation of “church” has cause innumerable errors.
Maybe it depends upon the translation one uses, however, Jesus did sa , “upon this rock, I will build my church, and the gates of hell shall not prevail.” This doesn’t refer to the Catholic Church as they like to erroneously teach. Paul addressed different churches and the Book of Revelation contains the words of Jesus to the 7 churches. My dispute is with people referring to their place of worship as the church - when the church is the body of Christ, regardless of the name over the door. (providing they are a Bible based one, of course).