CloudFlare's Browser Integrity Check (BIC) is similar to Bad Behavior and looks for common HTTP headers abused most commonly by spammers and denies access to your page. It will also challenge visitors that do not have a user agent or a non standard user agent (also commonly used by abuse bots, crawlers or visitors).
This feature can be turned off under the Firewall app -> Web Application Firewall.
Alternatively you can visit this URL to visit the page directly: https://www.cloudflare.com/a/firewall/<yourdomain.com>/waf
You are also able to selectively enable or disable this feature for certain sections of your domain by implementing a page rule. For example, you may want to disable this functionality for the section of your domain that hosts your API.