Server build cannot execute unit tests due to failure to create .mdf in TestResults folder

I have a build server with Visual Studio 2013 Premium. I need to build an ASP.NET MVC 5 solution (.NET 4.5.1) on this server. The builds are currently hanging at the test execution step, according to the build log. If I disable test execution (specify <RunTest>False</RunTest> in TFSBuild.proj) then the build completes successfully without issues.

If I launch Visual Studio on the server (run as admin), compile the solution and execute the tests there, I get the errors below:

CREATE FILE encountered operating system error 5(Access is denied.) while attempting to open or create the physical file 'D:\c\43\productname\branchname\Sources\Source\solutionname\TestResults\solutionname.TE.Tests.mdf'. CREATE DATABASE failed. Some file names listed could not be created. Check related errors.

This TestResutls folder (and the entire D:\c directory) has full permission for all relevant users and more: tfs12build, tfs12setup, NETWORK, NETWORKSERVICE. I've installed SQL Server 2012, which did not help. Any idea why I'm getting this error?