It's actually not really a big problem. Here are a couple of things that I do in these types of press conferences:
First of all, believe it or not, most of the flashes are set to similar settings and if you get two, three or even four flash burst while your shutter is open the impact on the exposure is minimal. Usually at press conferences you want to be shooting at a somewhat fast shutter speed (as in 1/250 the minimum) because motion blur is unacceptable to most editors in this situation. You're not there to get artistic with it, you're there to get a clean, crisp image. The speaker usually isn't moving much, but they often wave their hands around when they talk and that can blur with anything below 1/250.
The second thing I do is often times shoot without a strobe and set my white balance to Auto mode (I work with top of the line Nikons which can handle the variations) and then expose manually for the bursts. Sometimes this effect will give you the perfect exposure you're looking for. I have worked a few press conferences where the Auto WB gave me a blue tint when there were a number of flashes firing at once and TV camera flood lights on the scene, but again, it wasn't anything that couldn't be corrected easily in post.
In the end, I prefer the multiple blasts. The different light sources from different angles can give you cool shadows, believe it or not.