While the original question was about using a table saw, this is also an issue for using a router table and it's about fence adjustment. I have an Incra fence on my RT (Incra LS) and it allows micro adjustment down to better than 1/1000". As was said earlier, when you get down to micro adjusting, bumping a traditional fence accurately is pretty close to impossible. And, if you bump too far, it's impossible to get back to where you were before bumping. However, the Incra fence can do much much better. Once you have used that level of control, anything else seems stone age crude.
Yesterday I was using my router table to cut a centered slot in the ends of some frame pieces and, after a bit of setup and test, I got it spot on. Cut using the flip once method - get the bit super close to centered, cut, flip, cut. Then I cut the matching tenon using the flip method described in several previous posts - cut, flip, cut, test, tweak, repeat. Dead centered and perfect degree of tightness. Tweaking was done in multiples of 1/32ths of 1/32" (ie, multiples of 1/1024").
While 1/1024" is in the noise level, fractions of 1/32" aren't. Especially because, as was pointed out above, you are doubling the movement with the flip. If the Incra table saw fence wasn't so huge I would have it in a heartbeat. Not because of the need for 0.001" accuracy but for that level of precision "tweakability" and 1/32" repeatability.
By the way a good router lift will also give you this level of tweakability for the depth of cut.