I have a Nexus 7 and a MacBook Pro running El Capitan (10.11.6). I just installed Android File Transfer (1.0.11) and connected my Nexus.
Result: Android File Transfer automatically opens, but says:
Can't access device storage.
Make sure your device is unlocked and "File Transfer" or "MTP" mode is selected.
I found Google's troubleshooting page, and updated Android as per the advice there. I'm now running Android 6.0.1 with security patch level August, 2016. I got the same result.
My device was unlocked and there was no notification on the device when I connected it.
I found https://android.stackexchange.com/a/125679/190389 and followed those steps, but found that MTP mode was already selected, so that wasn't the issue.
I tried with more than one USB cable; one dinky cable resulted in the computer not recognizing that the device was connected at all (i.e. the device charged but Android File Transfer didn't open automatically, and when opened manually it said no Android device connected). But the cable resulting in the error message above was a sturdy good one that I got from WASD Keyboards along with my high-end keyboard purchase.
How can I get Android File Transfer working?