The test was previously an integration test, relying on luck and many
goroutines and lots of time to hit the path to be tested.

Instead, rewrite the test to exactly hit the path to be tested, in one
try, in one goroutine.

Fixes #18205

Change-Id: I63cd513316344bfd7375dcc452c1c396dec0e49f
Reviewed-on: https://go-review.googlesource.com/35107
Run-TryBot: Brad Fitzpatrick <bradfitz@golang.org>
TryBot-Result: Gobot Gobot <gobot@golang.org>
Reviewed-by: Ian Lance Taylor <iant@golang.org>