your question is maybe about any impedance mis-match.
like.. if the cable box has been there long enough, will a different connection be bad for the cable box.
i dont think there is anybody here that claims to be giving such insightful information.
generally, those inputs are supposed to be within range of eachother.
and the cable box is supposed to cover the entire range.
however, with age.. the cable box might not support the entire range anymore.
say the mitsubishi tv is at one end of the range, and the cable box refuses to send a signal to those inputs.
but if the toshiba inputs are different in the range.. the cable box might work fine with the toshiba, and cause the mitsubishi television to appear as if there was a problem with the inputs.
if you have ever known an electronics repair person and mingled with them.. it is usually best to go back and have them check for any future problems of age/decay.
it would be upsetting to have the above example true.. and with the cable box connected to the toshiba, the toshiba actually break because of the cable box.
kinda like having one problem piece of hardware cause two broken pieces of hardware.