Agree with all replies on here... sounds like a shady dealer to sell you a car with known issues, and what else has those issues caused? Bad shaking would have me wondering about manifold flanges, exhaust/downpipe movement, etc. Cleanliness is one of the worst things to go by when looking at a used car as it's very easy to polish a turd. The Si can be a bit harder to come by than a base Civic, but there are still plenty out there - don't settle for one that has an obvious and known issue.
I've rushed in to buying used cars in the past and was bitten by each one.
Best of luck with the hunt!