I dont think NK cells respond to MHCs in classic sense as do say T cells: Cell with MHC + Foreign protein recognized by TCR leading to T cell activation and death of Cell.
NK cells killing ability is inhibited by MHC I.
NK cells are usually found closely associated with Dendritic Cells in lymphoid tissue and inflammation sites. Dendritic cells can activate resting NK cells by secreting IFN, and IL 12, 15, 18. Up regulation of MHCs and NK cell activity simultaneously would be better for proper response. All the normal cells will increase their MHC and would not get killed by mistake. Tumor cells or infected that has lost the ability to make MHC I will not be able to respond to the IFN and will stand out even more.
Some viruses use this to their advantage. Certain strains of HCV actually cause infected cells upregulate normal MHC I. This allows them to escape killing by NK cells.