When I was a kid (US), my dad told me that improperly rinsed dishes caused stomach issues, so I'm an avid rinser. I think the same action that causes the oil to slip more easily into water (soponification) is the idea behind it causing faster "digestion transit". No clue if it happens in practice, and I am not a chemist (just a physics student who hates organic chemistry which this would fall under). But more than that, the idea that it rinses off the grease and food bits is a good reason to do it. If people are interested in saving water, they should forget about forgoing rinsing and invest in a dishwasher as it saves a lot of water.
Not all British people don't believe in rinsing. Aggie and Kim tell people to rinse their dishes in hot, running water, and my very British husband is a rinser. To me it's not an anti-British thing to think it's weird to not rinse. I don't have a problem with countless other things that are different here. Rinsing is a bit of a hygiene thing and you're usually putting others at risk by not doing it.