You just cannot understand.
We are saying that anyone can go to the Bible for instruction on being a Christian. They do not need to be Catholic, Baptist, Presbyterian, Methodist. When they go directly to the Bible and follow instructions found there - they are Christians.
Now - that is what the Church of Christ (the group of churches with that name on the door) has done. So they are really just Christians - not a member of a denomination. That is why there is no governing board, no central headquarters - just stand alone congregations. Some congregations may err and make mistakes but that does not affect the other congregations. This allows the church to remain true to the Bible. Each group of elders lead from the Bible instructions.
Now - of course, when you go to the Bible and follow what God says - you are doing what God wanted and will receive salvation. So, we are the same as that person who just read the Bible and followed the instructions to be a Christian (not Church of Christ, not Methodist, Catholic, etc.)
If you will just get away from denominations and understand that we claim we are not a denomination - we are just biblical christians. So, when we say we are following God's instructions, you bet we are and therefore the claims that we are correct are true. Why wouldn't they be?
Why do you more readily believe what your denomination tells you than what God tells you in His word?
Don't you think that the CofC is a denomination? I do.
You might claim it, but it isn't true.