I don't think it is user agent based. I think they just detected some js wasn't run by the browser.
I don't have any godaddy account to try it out but I very often get captcha to respond on on websites with a message saying my browsing has been flagged as possible bot access. I am using ghostery on firefox.
Cloudflare has started kicking people who forge or don't send their referrers. I'm pretty sure they'll ban you (based on customer configuration) if your user-agent doesn't match their fingerprinting/probing.
I don't have any godaddy account to try it out but I very often get captcha to respond on on websites with a message saying my browsing has been flagged as possible bot access. I am using ghostery on firefox.