That's not something I have encountered either - but I agree with AVG's suggestion that the voltage reference might not be as stable as you would hope. The other possibility being the higher current in the backlight circuit is being coupled to the measuring circuitry by some means - which, if it were the case, would suggest either a poor physical layout, a faulty component or a component not fitted properly.
I am curious as to whether this phenomenon is better/worse at different ranges and is/isn't proportional to the measured quantity.