I have no idea what Coppy's bosses are telling him, or if there is even any pressure like you suggest coming from the higher-ups. If anyone thinks Swanson and Albies should start 2017 at the MLB level, whether that person is Coppy, Hart, JS, McQ or Mr. Liberty himself, then that person needs to be removed from their position. Just because they are higher ranking and in a position to get what they want does not make them right.
It would be different if the team were truly going to compete for a playoff spot like they were Heyward's rookie year. I can understand wanting the best players possible on a contender, even for those few weeks, so it was at least defensible (yet still incorrect) to burn a year of Heyward's control in order to get into the playoffs his rookie year. However, the 2017 Braves will be competing for a .500 record, not a playoff spot, so there is zero reason to burn a year of control for Albies and Swanson in 2017.