According to the official App Engine's Traffic Splitting docs, it seems possible to achieve a 0.1% precision for traffic routing:
Using cookies to split traffic makes it easier to accurately assign users to versions. The precision for traffic routing can reach as close as 0.1% to the target split.
However, the UI seems to only allow 1% (see image below).
Are the docs wrong, or am I missing something?
You seem to interpret precision as the resolution of the target value. It's actually the difference between the target value and the actual value(s) you get.
So for a 1% target value a 0.1% precision means you could get actual values between 0.9% and 1.1%.
But technically the statement doesn't really say very much - it's not a guarantee, so it leaves room for pretty much any precision ;)