I would say yes they can.
When you have an accident which is your fault, in effect the other person sues you for the damage.
You, in turn, go to your insurance company and ask them to give you the money to pay them.
There is an excess on your policy which is effectively the most an accident will cost you - the insurance company will pay the rest.
Supppose you have a £1000 excess on your policy, your car is worth £400 and you cause £3000 of damage to another car.
In this case you put in a claim for the cost of repairs to the other car plus the write-off value of your car - £3400. The insurance company knocks of the excess leaving £2400 and send you that amount.
Unfortunately the repairs to the other car are £3000, so you need to add £600 to pay the claim.
In reality, of course, the insurance company pay the other person directly but if you think about what is really happenning you can see why the insurance company are asking for money from you.