To elucidate the mechanisms behind the enhanced T_{c} in monolayer (1 ML) FeSe on SrTiO_{3} (STO), we grew highly strained 1 ML FeSe on the rectangular (100) face of rutile TiO_{2}, and observed the coexistence of replica bands and superconductivity with a T_{c} of 63 K. From the similar T_{c} between this system and 1ML FeSe on STO (001), we conclude that strain and dielectric constant are likely unimportant to the enhanced T_{c} in these systems. A systematic comparison of 1 ML FeSe on TiO_{2} with other systems in the FeSe family shows that while charge transfer alone can enhance T_{c}, it is only with the addition of interfacial electron-phonon coupling that T_{c} can be increased to the level seen in 1 ML FeSe on STO.