It's a perfectly plausible situation and I would imagine it fits the majority of most private car seller's circumstances. People tend to buy a car, then their old one up for sale whilst they're using the new one. Most people who buy a car will not take out insurance on two cars because 1) it's pointless and 2) their no-claims can not not generally be used on both of them).
Ah, in that case - my apologies; I've made the usual mistake of not basing my opinions on your own personal experience :)