I snaked my kitchen sink drain to the end of my 20' snake so I know there is no clog for 20'. When I run water into the sink it starts to fill up immediately - not enough time to fill 20' of pipe. When the dishwasher drains it begins filling both sides quickly but only for an inch or two. This has been a problem ever since we installed a double sink. I'm tempted to install an air gap (aerator) for the dishwasher but I don't see how that would help. There is no problem with the vent since my vent is in the wall behind the sink (with a one way valve) because I took the valve off, snaked the vent pipe, and that made no difference.
After the sink fills a bit it will stay full for a few minutes and then at some point when the water gets low enough it will drain a little faster - that is why I think there needs to be an air gap to break a siphon but again I don't see where the siphon is happening.