Whoever came up with those definitions, sure didn’t have an agenda. </sarc
The truth will always apppear as an “agenda” to whomever disagrees.
The real question is, where specifically do you see an error?
The Catholic Church receives the Baptismal records from Protestant Churches when one joins their ranks.
Hardly something one would do for a person coming from a non-christian faith. (note they DO NOT accept LDS baptism)
I won't even get in to the Trinity piece. It is a strong as ever in the mainline Protestant movements save some liberal American influences whose time maybe running out thank God.