As luck would have it, I ran into this exact issue this morning submitting a case.
I received the same error about the CAPTCHA. In my case though, the 'I'm not a robot' box appeared below the case description field and I was able to check the box.
It appears that Meraki is using Google's reCAPTCHA in an invisible mode. I'm guessing that if you don't 'pass' the check when you submit the case, the checkbox is supposed to appear, so that you can assert your non-robot-ness.