Full control means a full node, end of story. Anything else is a compromise where you are trusting X to do Y: not good.
Thats not true at all. As long as you are in control of your private keys (doesnt matter if they have been generated by a core wallet or by any other wallet)
you are fine and can decide for yourself which "chain you follow".
And additionally al ot of wallets provide both chains (e.g. electrum if im not mistaken).