T Cells Specific?

[kevinsmith6086]

I had previously learned that Cell mediated (T-Cell) and Humoral (B Cell) Immunity were specific responses. The video disclaims this and says that T-cells are nonspecific. If this is true, why do they produce memory cells?

PS: I learned nonspecific were physical barriers (skin), macrophages, monocytes, inflammatory response, interfereon, etc.