Yes, so long as certain facts are met, insurance companies can absolutely be sued and held accountable for their wrongdoing. Remember, all insurance policies are contracts. In other words, your insurance company promises to pay money in the event of an accident, and in return, you pay a premium. In South Dakota, the law says there is an implied covenant of good faith and fair dealing in every contract. When that covenant is violated, it is considered bad faith, and opens insurance companies up to lawsuits.
Simply put, insurance companies must put the people and entities they insure first. They must act in good faith and deal fairly. When they do not, legal action may be taken.