Garp,
Your multitester do not have a DC blocking capacitor on its AC setting, which explains the anomalous readouts. Try a not-so-el-cheapo digital multitester.
I have an el-cheapo digital multitester and find it lacking DC blocking capacitor and therefore reads incorrectly, similar to what you observed. It simply half-rectifies the signal so that reversing the tester leads would read zero. But my Radio-Shack multitester correctly reads ripples.
And yes, your notion is correct, after AC has been rectified and filtered by a capacitor, there will be pure DC at the capacitor terminals if and only if there is no load at all, i.e., there is nothing to discharge the capacitor. As soon as a load is connected, ripples will appear at the rails.