Perfectly "clean" rainwater should have a pH close to 7.0 -- being pure water. 5.6 is bordering on "acid rain". (I'll check my rainwater sisterns, but they've had a long time to settle.)
Yes, sea water is highly buffered. However, that buffer is not instant. Look at the small scale in my (freshwater) aquariums... they have carbonate buffers in there (a lot of it, in fact -- aragonite and commerical buffers) and the pH can still dip below 6.6. If I draw a sample for testing, sealed in the tube, the pH will slowly recover to 8.4 as the disolved buffer does it's job. A great deal of the buffer capacity of the oceans are the coral in them.
But yes, I agree, CO2 is not what's going to destroy our oceans. We've been doing far, far worse things to them for a long time now.