You know a good way to spot when an explanation is just an excuse? It keeps changing.
Direct Line tells us they're not on price comparison websites. Indeed, the company has been boasting of its refusal to compete on price for rather more than a year now.
The reasons an insurance company might not to appear on price comparison websites are, admittedly, more complex than a mere desire not to compete directly on price. There are potentially sound business reasons to want to own the customer relationship. But since those reasons are mostly to do with preventing the price comparison site from selling those customers cheaper insurance from a new advertiser at the end of the year, they aren't an explanation you can tell the customers themselves. So over the course of more than a year we have seen, instead, a series of bizarre excuses.