I fixed this by implementing something similar to user2934013 answer, but I will try to explain in more detail:
My problem was that I was trying to run unit tests and I saw a "make before run" error. Removing minSDK is not possible for me because I rely on backward compatibility. I just started to see the problem after upgrading to Intellij 13.
It looks like I created an Artifact for my Android project and checked "Build on Make". For some reason, this ran counter to unit tests (but not regular builds for an emulator or device). I unchecked the artifact settings and the problem disappeared.
There is probably a way to fix the build order, so this works correctly, but I'm not good enough at setting up the Artifact build to know how to do this.
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