The fine print excludes cover for injury where the rider was not obeying the road rules:
We will not pay for any Injury directly or indirectly caused or contributed to by, or in the consequence of ...
... engaging in illegal activities at the time of the Injury or not complying with the road laws
and/or legislation applicable to the State which they are cycling in;
I asked for clarification of this from CycleCover (as they do a specific cover for BQ members) and they confirmed that you must abide by all road rules and regulations. (Note I only found this clause in the BQ specific cover).
So in the context of this Channel 9 story about BQ membership, sadly it seems the rider might not have been covered anyway. From memory, the story said he lost control of the bike on a corner and went over a railing where he unfortunately sustained some very serious and permanent injuries Losing control of your vehicle and crashing is against the road rules, hence his injuries would not be covered, eg.
297 Driver to have proper control of a vehicle etc.
(1) A driver must not drive a vehicle unless the driver has proper
control of the vehicle.
So in a multi-vehicle accident the only time you are covered by this insurance is if the other party at fault, and then you have their compulsory 3rd party insurance for your injuries anyway. For single vehicle accidents coverage is going to be very hit and miss as you would need to avoid breaking a road rule, such as 297 above and would also include the dangerous/careless driving provisions in the Transport Operations (Road Use Management) Act 1995, not just the road rules regulation 2009.
My car insurance covers me when I'm in an at fault accident, that's the whole point (with exceptions around drug&alcohol use and driving unlicensed)...
Originally joined BQ for the insurance, now I'm probably going to switch my commuter over to the cover on my home&contents... after reading the fine print there!
Edit: For extra clarification, I'll re-iterate this is a specific clause added for BQ membership insurance, its not part of the standard CycleCover insurance.