This is not correct. The 24-hour refund is available to everybody.

When airlines started requiring immediate purchase and offering 24-hour policies in an attempt to thwart regulation, CO had a policy that they would only do it for OP members logged into their account at the time of booking. It seemed like a technicality to not offer it to everybody. I wonder if that's what you're thinking about.

Later, CO dropped that restriction and made it available to everyone (which was more inline with what most other carriers were doing). UA's was always available to everyone.

History aside, the current policy is here, and it applies to everyone, irrespective of membership or logged on status.