Are PHPUnit Functional tests in conflict with the build container model?

[grayside]

From discussion:

Trying to run a functional test, and I'm running into a bug:

1) Drupal\Tests\schemata\Functional\RequestTest::testRequests
Exception: Warning: mkdir(): Permission denied
Drupal\Component\PhpStorage\FileStorage->createDirectory()() (Line: 157)

I don't see why this should happen, but it looks a bit like https://www.drupal.org/node/2760905. It's believable to me that our build container/web container split could run into a problem with this.

This is a blocker on using an Outrigger-based development environment to address https://www.drupal.org/node/2910720