We demonstrate that there is a relation between the Curtis-Tits theorem and Phan's theorems that goes beyond the similarity in appearance. We present a geometric construction connecting those theorems and suggesting that Phan's theorems can be thought of as "twisted versions" of the Curtis-Tits theorem. The construction itself further suggests that Phan's theorems are only some of many possible such theorems. We make this explicit by presenting a new Phan-type theorem for the symplectic groups.