Executive Meddling: Zig-Zagged. Devs from Core Design were working on 10-year anniversary project mostly in their spare time, but after getting enough material to actually present it, they've went to Eidos to strike a deal for publishing. Eidos not only send them away with nothing, but seized all the material and handled it to Crystal Dynamics to start working on the game anyway. Thing is - while it didn't sit well with fandom and was generally a dick move, Eidos had every right to do so, as the legal owner of the franchise defending their own property.
Money, Dear Boy: Toby Gard, the mastermind behind original game, was again hired by Crystal Dynamics as a consultant to help them, but limited his influence to bare minimum and voice-over for extra content. He later openly admitted he took the job only because he needed the money. He also went quite vocal how while working with Crystal Dynamics is enjoyable (he was part of the creative team of all their initial games and later won few awards for his script for Underworld), but the sole concept of remakes simply doesn't appeal to him at all and he would rather not talk about it at all.
What Could Have Been: The whole concept for the project and initial stages of it were done by Core Design, in their pitch to either get back to the franchise or at least deliver remaster of the first game. From all the leaked material, the game looks like a genuine remaster, simply applying modern technology to the original, but keeping Core's trademark complexity of levels and not touching the plot or characters that much. This is in stark contrast with Broad Strokes approach of Crystal Dynamics, with all of the game's content rebuilt and re-imagined from the ground up, making a lot of changes that didn't sit well with fans of the original, tying the story with their overarching narrative and, which alienated fandom the most, greatly shortening and simplifying all the Marathon Levels.