Difficulty drawing pixel-accurate images in iOS 10.1 GLES2

When I draw an image that's made up of alternating black and white pixels like this:

    for(int y = 0; y < h; y++) {
        for(int x = 0; x < w; x++) {
            bool on = x % 2 == 0 && y % 2 == 0;
            img.setColor(x, y, on ? ofColor::white : ofColor::black);
        }
    }

(Inverse of the pattern here.) Then I get moire patterns.

The above test is with ES2 and with 4-sample antialiasing enabled. Disabling antialiasing changes the pattern but does not remove the moire. ES1 does not show a moire pattern regardless of whether antialiasing is true or false.

I checked out the latest OF, pulled libs, and created a project with the project generator (copied from the 0.9.8-ios release). I'm running iOS 10.1 and XCode 8.1.

If I add the line ofSetupScreenOrtho(ofGetWidth(), ofGetHeight(), -1, +1); at the top of draw() then everything is ok on the real hardware. In the simulator the pattern is still "blurry" (instead of a 2x2 square being [255, 0, 0, 0] it's [149, 43, 43, 17]) but there is no moire. I tried checking if the difference between the hardware and the simulator is due to floating point accuracy, but I think it must be the graphics card. Because the matrices computed by ofSetupScreenOrtho() are exactly the same.

Start by reproducing the alternating-pixel image on iOS 10.1 with GLES2, comparing 4-sample antialiasing, no antialiasing, ES1, and the simulator. The issue names no source files or tests; done would mean determining the cause and eliminating the moire without relying on ofSetupScreenOrtho().