The DMPC is an idiot, so the players always ignore what they suggest?It has been a consistent problems in games I play and this is the reason why. If you have a DMPC and that character is a core part of the party for balance/mechanics reasons there are really only 2 ways to play it.
1. One is the DMPC makes no decisions at all. In this case it is not really a character, it is just a set of skills the party uses to cover gaps. It rubber stamps whatever the characters do and the characters can use it however they want more or less. The party decides what magic items he gets, the party decides where they go, what they do. The character is essentially a party familiar or a meat shield.
2. The other type is the DMPC that makes core decisions and they can't really be vetoed because they need the DMPC to play the game. This is what you are talking about in the quote above. A realistic, fleshed out character is going to have opinions and there is going to be friction between that character and other characters, just like there is between PCs. As a DM though if you are playing this out there is a huge power imbalance.
An NPC that is part of the story is different. They are not there to round out the party, they are there for story purposes.