Finny pretty much concludes that Gene probably is responsible for knocking him out of the tree. Even if Gene did it accidentally, it is understood between the both of them that Gene may have had subconsciously wanted to do it and this helped push him over the edge. They treat it as a moment of weakness.
You might find it unsatisfying because it would seem more logical for Finny to just turn his back completely (and immediately) on Gene and that Gene would be more remorseful at first and a little more forthright and honest about from the time of the incident until the end of the novel. But feelings are involved and they are both adolescents which can be an awkward and confusing time. Finny is still clinging to the innocence of his youth (he continually jokes that the war is a big joke and has always been the one to make school life more imaginative and fun – some critics say the “separate peace” is this youthful atmosphere that Finny creates all around him – separate from the rest of the world and the war). Gene is not clinging to his youth as much but is still trying to figure out who he is. Plus, Gene’s relationship with Finny has always been conflicted with feelings of envy, anger, and love. It’s as if Finny represents Gene’s youth and innocence. Gene’s conflict is that he wants to cling to this but wants/needs to abandon it. So, both of them never really make complete sense of it because of all these conflicting feelings. They seem to just accept that it happened and that such things just happen when kids play rough or when feelings are involved; as inevitable as growing up.