Jacqui.c said:

Quite often it is cheaper for an insurance company to pay off a claimant, even if they suspect that the claim may be false to some degree, because of the cost of defence.

And it's worse than it appears in what you said.

The insurance company doesn't worry about what they pay out in nuisance value. Why? Because the poor insurance customer is now, with the paid claim in his file, "a poorer risk", so the company raises his premiums!
Not only that! That paid nuisance claim (along with the rest of its ilk) goes into the statistics from which the underwriters compute everybody's insurance rates! The company may actually make money by paying a bad claim!

Conversely, if they deny the claim and get sued, they have big attorneys' fees to pay. Oooh, watch out! The insurance lawyers may defeat the lawuit, and that's bad too! Why? Because now the company is out its costs, but doesn't get the advantages detailed in the preceding paragraph!

Dave Oesterreich