Keith &Tony, I think you both have it half right.
Our rudders work fine as long as you stay ahead of the wave on a "clean" shoulder and point it just right (Keith's suggestion). For me that's about 20-30º max. You can't stay there forever though. Beyond that angle, I am ready to exit the wave before it crashes.
Once the wave breaks, or catches up to you, you typically lose some rudder control due to reduced (or even reversed) water flow over the rudder. It's a temporary situation and does not mean an automatic broach. You you still have momentum, a planing surface with some keel, 2 Amas and a sail to help steer the boat. Using your mirage drive can help too.
There are several dangers that would tend to cause a Huli while surfing.
The first is "perling" the bow at the bottom of the wave, which rapidly slows the front of the boat and causes a train wreck to begin behind you. We experience this "porpoising" all the time while surfing open water wind swells less than 6 ft. Keith is well aware of it. If you can stay pointed basically straight ahead (as Tony suggests), you will slow down, dig in and the wave and whitewater will usually pass over you. It might even bury you. If you choose to twist the rudder at the last moment, or are already too parallel to the wave, it WILL jackknife the boat. At that point, if your sail is still sheeted, and you use tramps like yakman, your sail will suddenly fill with air (on a reach) and your windward tramps will fill with water pressure. You now have a great recipe for a Huli.
The next danger is a plain old broach, usually at the top of a steep wave, where you lose rudder control because the blade actually leaves the water, or is neutralized by waves catching up and passing you. Even if you are doing 10 mph with the blade submerged, the 20+ mph flow of water from behind causes the rudder to momentarily lose grip. You go from having a super-sensitive rudder to having little or no control at all. Sensing this, you start to overcorrect.
The stern wants to come around and is gladly obliged by the wind and whitewater. Monohulls with big daggers/keels tend to experience this more, (Tonys point).
Lastly, whenever you exceed your hull speed, or "brake" suddenly, you could easily break a rudder pin or Aka brace. My old twist and stow rudder used to stretch and "pop" loose when I hit speeds over 15mph and would screw up an otherwise decent ride.
All waves are different. Reef breaks and shore break waves are different from channel sandbar waves - and very different from mixed open ocean swells.
Our Hobies surf like pigs on all of them, so be selective, steer with your sail as much as possible - and expect surprises.