Has there been any instance where a national record in any sport broke the world record?
Yes this is present in shooting where there is a list of National records that surpasses the world records.
this is because of the very strict regulations followed by "International Shooting Sports Federation"(ISSF). They only consider those events for world records which are supervised by the ISSF(like Olympics, World Championships, World cups, Continental Championships, etc). On the other hand, most member federations have more relaxed rules for their national records. This creates many more opportunities for record-breaking, especially so in the non-Olympic events, where World Cups are not held.
for the list of such events and the details of the National and World records have a look on the link below.
and still it says that the list is incomplete, so I guess there are more out there.