The CofC in America sprouted up during this country's early days, much as most of the American denominations did. They (CofC) claim to be the one true church tracing back to the days of christ b/c of there belief structure, dogma etc... Speaking purely as a historian, the Catholic Church is the only group that can trace back that far, but I really think you need to mark a line between those times at the council of Nice. It would be more fair to assert that they are a decedent of Martin Luthers....
Yes I was a Church of Christ member and found the dogma as unnecessary as Martin Luther found the Catholic Church wanting.