I could not find many details on this 14-day rule but all the sources I found, including the EU website suggest that it only applies to people who are just moving into the country. So it means you must register the car/motorcycle within 14 days of becoming a resident, and not 14 days of importing the vehicle. Basically, it seems it's intended to cover a car you would use to move into the country.
Proving that you only registered as a resident in the last few days would seem relatively easy but of course that's not your case. Nobody is expected to prove they brought a car/motorcycle into the country recently even though they already were a resident because in this case another procedure applies.
Once you are a resident, you cannot drive a foreign-registered car in the country without declaring it first, even for a single day. SKAT, the Danish tax authority has a web page on the procedure to follow when importing a foreign-registered vehicle as a Danish resident.
The first step is submitting an online form even before you bring the vehicle into the country. You need to print the receipt and to keep it in the vehicle. That's how the police can check whether you are currently importing the vehicle and waiting for the inspection/paperwork or driving it illegally.