Ok, so I took the station down and mounted it on a much more stable platform (although not totally rock solid). Tested with a sprinkler and all looked to be fine.
Then I took a syringe and looked to see exactly how much water it took to trigger the bucket to tilt and register, thus getting a known amount of water. Then what I did was put in half the known amount of water and then shake the station fairly vigorously without getting the bucket to tilt and register. It was plainly obvious in doing so that water was being released from the bucket without it registering.
I then put the exact amount of water from the previous experiment from the syringe, and it triggered a tip. I did this a few times but my conclusion is that the rain gauge is a lot more sensitive to shaking than I gave it credit for, and that the big problem with an unstable mount is not the bucket tipping, but its failure to tip because water is released from the bucket.
I'm keeping the station mounted in its current location to wait for the next winter storm in a few days time, and will compare with a standard rain gauge. If all good I'm going to have to find another location because the test location is a poor one for wind.
So basically lesson learned... When they say mount in a stable position, they mean a REALLY stable position.
Also another lesson learned. All in one weather stations are great and convenient, but the locations that are suitable for one sensor aren't always suitable for another.