I have never quite decided what an event photographer is. Or what an event photographer does.
An infantry assault over open ground in the face of machine guns is an event - likewise a wedding is an event, similar to the infantry assault, but with the officers up at the front...and generally at a wedding the machine gun fields of fire overlap more...
So what does an event photographer need - besides nerve, a camera, and a hip flask? Well they either need a long lens to stay out of the way or a short lens and a flash to get in amongst it. Those of you given to fits of horror at the thought of flash may be excused - you are artists and we make allowance for you. The rest of you need to see what is actually going on.
Nearly every serious camera has some form of hot-shoe connection on it. This can be the place to put your flash if you want the light to blast straight forward. Good for police mug shots but a bit limiting for some other subjects. That hot-shoe connection is a useful place, however, to base a wireless control for your flash - and then you are as free as the air to place it anywhere that helps.
Hahnel, Promaster, Yongnuo, Pocket Wizard, and a dozen other small manufacturers make wireless flash triggers that do the job. The expensive versions have TTL connection between the flash and the camera while the economical models just send a "fire now" signal to the flash gun and you have to do all the power setting on the flash yourself.
This is not onerous on some flashes - you can lock Nikon, Fujifilm, or Canon flashes into "manual" mode and then use the button or dial control on the flash to go from 1/1 power down to 1/64 power. You get a quick feedback from the LCD screen and soon recognise how much power you need.
The greatest joy of this unleashed approach is that you can operate a light camera with one hand and then hold the flash in peculiar and particular positions to punch light into the scene. You can even abandon it to point in out of reach - as long as you can prop up the rig.
No-end of scenes benefit from fill flash - in some cases even to the extent that the fill becomes the dominant light.
If you free yourself from the top of the camera you can light anything!