Quoted: I guess my real question is. Will she get another TV with the same issue (minus the speaker buzz)?
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Very hard to tell.
While the speaker buzz is probably just a mechanical issue with only that set, the high pitched noise might be something that all the sets could experience.
When the set is running it applies a certain "load" to the power supply. When the set is turned off the load is reduced but it is quite possible that the power supply is still running to keep certain electronic circuits functioning in standby mode. When in standby mode some switching power supplies will throttle back to burst or discontinuous mode for higher effeciency - sometimes this causes ringing or high pitched oscillation, usually not harmful but definitley annoying...
This could be common with that particular set - or not..