I'll present one model for thinking about Japanese passives -- hopefully it will help.
Consider the underlying active sentence:
誰かが [私の]背中を 押した。
To make it passive, you demote the が-marked argument to に, and then pick something from the sentence to promote to が.
If you promote 私の to 私が, you get A. If you promote [私の]背中を to [私の]背中が, you get B.
A: [私が] 誰かに 背中を 押された。
B: [私の]背中が 誰かに 押された。
In passives, the grammatical subject is the thing "being affected". In sentence A, you are being affected by your back being pushed by someone. In sentence B, your back is being affected by being pushed by someone. Hopefully that explains why two different things can work as the subject.
Sentences like A, where the subject is the person, are often referred to as the "adversarial passive", due to having a connotation that the person was negatively affected by the event. Since in sentence B, "your back" is the thing being affected, you being affected is not explicit (although the sentence certainly doesn't negate that possibility).
If you'd like to hear more about this model, I've written about it more in my answer to 「を」 object marker in this 受身形うけみけい sentence. If you'd really like all the details, you could also read Ishizuka, T. (2010). Toward a Unified Analysis of Passive in Japanese: A Cartographic Minimalist Approach.