They expect attacks from any powerful channeler they meet, Light or Dark, so they're ready to fight back instantly. A great example (and there are many) is Cyndane's scene right before the Cleansing. She feels the Choedan Kal being used, cuts the top half of a man's head off mid-sentence and has a gateway open before the body even hits the floor. All this when she was alone with a non-channeler, a relatively safe situation for a Forsaken.

The proximity can easily be explained with inverted weaves, and Forsaken are most likely in the habit of using inverted weaves, probably to the point that their "default setting" is to whip up an inverted [gateway]/[fireball]/[razor-thin thread of air]/[shield]/[Compulsion]/ etc.

If you're looking at non-Forsaken suspects, the speed thing still most likely applies, not as strongly as with Forsaken, but combat ready channelers are still very fast. And the proximity can actually work in their favor, since any Rand-aligned channelers that detect channeling will write it off as another Rand-aligned channeler using the Power somewhere else in the Palace.

Your number 3 reason is basically number 1 restated, or at least, explained again by combat-ready channelers reaction times.