NUnit Testing with Action and Lambda

I have been reading up on Actions and Lambda expressions on MSDN but there is still something I am missing. I have the following public class.

public class ExitChecker
{
    public Action EnvironmentExitAction { get; set; }

    public ExitChecker(string[] args)
    {
        if (string.Compare(args[0], "-help", true) == 0)
        {
            EnvironmentExitAction = () => Environment.Exit(0);
        }
    }
}

And I have the following test class.

[TestFixture]
public class AVSRunnerConsoleAppTests
{
    [Test]
    public void TestConsoleAppWithHelpArg()
    {
        string[] args = new string[1] { "-help" };           
        ExitChecker exitchecker = new ExitChecker(args);

        bool exitZeroOccured = false;
        exitchecker.EnvironmentExitAction = () => exitZeroOccured = true;

        Assert.That(exitZeroOccured, Is.True);
    }
}

I am attempting to test the Environment.Exit without actually calling the Environment.Exit. All seems to compile and run just fine but I can't seem to change the exitZeroOccured in the Lambda expression to true. Can someone point me in the right direction?