I think it must be a matter of semantics. In the broadest sense, anyone who successfully fires an arrow must push or their bow arm would collapse. Beyond that, you get different opinions.
Fred Asbell evidently thinks pushing with the bow arm is right up there at the top of things to do. In his book, he states that whenever his arrows begin to spread out on the target, the first thing he does is check to make sure he's pushing with his bow arm, and many times that solves the problem.
Arne Moe says don't push, just keep a solid bow arm.
Jim Ploen says the difference between a good archer and a great archer is how well they balance pulling with the string arm with pushing with the bow arm. Again, it must be a matter of feel, because under the laws of physics, I'm pretty sure the force against anyone's bow hand has to be the same as the force against his string hand, or the bow itself would move in the direction of the greater force. OTOH, I know how great an archer Jim Ploen was, and other expert archers have made a similar comment to me, so I'm sure they're trying to express something important, regardless of the laws of physics.
Obviously, you don't want your bow arm to collapse and push your bow arm shoulder up toward your neck. Nor do you want to hyperextend your bow arm shoulder and injure yourself. Somewhere in between must be a sweet spot, and it probably feels like pushing.