QARs get power from the AC bus. During a partial power loss, the QARs are not always load shed. Typically they will be un-powered when operating on standby power.
On aircraft that have non-integrated airframe computer systems (such as the A300 series, 737 etc) there is a data acquisition box (DAU) that converts selected analog inputs into digital signals and combines this data with any ARINC data bus signals for QAR and DFDR consumption.
Spurious data is very common in the outgoing data stream of most DAUs due to limited signal conditioning and lack of 'smart' A/D conversion. These acquisition boxes also use a relatively slow sample rate. Sampled analog inputs can be inaccurate to the point of requiring integration math (terminology?) to 'mold' the data to fit a known profile upon readout - not something I would wish to be judged by.
The majority of QAR (and DFDR) recorded data is of course reliable, but where there is an imperfect system used to collect and convert analog signals, there can be a 'perfectly recorded' stream of inaccurate data.