The way I understand it, flat panel TVs typically process each type of input differently, so there’s a chance that it will tolerate out-of-spec framerates on one or more of its analogue inputs. For example, my circa 2009 Samsung panel thinks 240p is 480i over composite and won’t accept it at all over HDMI, but it’s detected correctly via the YPbPr component input. Not refresh rates, but demonstrates my point that they’re not all treated equally.
As for expected framerates, for native digital video, I think 60Hz is typical; and I believe TVs are supposed to tolerate 60Hz±1% for analogue video, so 59.94~60.6Hz. (Framerates for analogue TV were normally 60Hz for black and white broadcasts, but later slowed to 59.94Hz to make time/space for colorbursts to enable color broadcasts while still being compatible with black and white sets.)