Another layman's question: As far as I understood, the T-cells recognize cancer cells and kill them because the two agents get injected directly into the cancer

Another layman's question: As far as I understood, the T-cells recognize cancer cells and kill them because the two agents get injected directly into the cancer site, where the T-cells are surrounded by cancer cells. Doesn't this have a risk of the T-cells misjudging normal body cells as dangerous if they happen to have any of them around, or if the injection happens wherewhere else than the cancer site? I'm thinking of (1) lower but high enough numbers of normal cells somewhere between the cancer cells, and (2) plain accidents like the needle pushed too far / not far enough.