The typical 7805 regulator does a good job of providing 5 volts, but does need a bit of spare voltage to play with. If the supply drops below this critical level, the regulator changes mode, and starts just dropping this headroom voltage. Most radios will just carry on working with what is left, more or less. The now imperfectly stable voltage might cause the timing circuits in both the radio and things plugged into it to not be as accurate as they were. If the voltage drops to the point where the radio no longer works, or more likely the servos, it doesn't really matter whether the radio is BEC powered or a separate battery, it will have nothing to give instructions to. I have had times when the servo was just capable of creeping about to signals due to an over extended sail, so although the battery was obviously low, the radio was still functioning.
Interesting about the switched mode thingys. Can the output and input lines not be fitted with decoupling components? The usual values of suppression capacitors spring to mind.