Redundancy of backup is my preferred approach. While my personal experience with tapping off the board is not THAT great, (and the diverse capabilities of the operators seeming to go toward lesser than greater) with good operators who know their system it is a wonderful asset.
However, as Murphy's Law dictates that anything that can go wrong will, I try to acquire audio backup via MORE than a single source, especially when setting up one camera for split input via each channel.
My good fortune is that I ALWAYS shoot a minimum of two cameras, and often three, dedicating one to mix from the board, and another to picking up live sound via both channels via either wired or wireless, sometimes even the on-board mic. In addition I have an arsenal of four Zoom H2 digital audio standalone recorders that do an outstanding job of acquiring GREAT source audio. These units have a broad range of adjust-ability and function, and like American Express I never leave home without them.
I am much more relaxed knowing I have extensive backup in the event any one (even two) of the options flake out, I have plenty of alternate options. Also, I will often use some or all of the various sources to lend depth and quality to what is sometimes a weak source from any one of the given approaches.
Keeps me safe, and my clients happy.