Also add a unit test to lock this behavior into the API.

Fixes #12016

Change-Id: Ib6ec6e7948f0705f3504ede9143b5dc4e790fc44
Reviewed-on: https://go-review.googlesource.com/15171Reviewed-by: Brad Fitzpatrick <bradfitz@golang.org>
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>