Please note that G12 refers specifically to the Alliance Platform, not the Alliance Starting Tile. Figure 3 in the Game Manual depicts the Alliance Starting Tiles, while Figure 5 depicts the Alliance Platforms.
I'm asking for clarification on if the alliance tile would have the same G12 rule as any regular field tile, such as legal pinning/trapping and pushing.
The Alliance Starting Tile is not treated any differently than any other field tiles with regard to Trapping. The Alliance Platform is not treated any differently than any other field element with regard to Trapping.
In short, would it be legal to push an opposing robot off their alliance tile in an non-destructive manner?
There are no rules prohibiting this, for either the Alliance Platform or an Alliance Starting Tile. The note in G12 is included because pushing a Robot off of the Alliance Platform carries with it a significant amount of risk that the Robot will tip over or become otherwise damaged.