For 'frivolous cases' to actually hit trial months of depositions, research, and meditations have to fail. If a case actually goes to trial it's because one side feels so confident in their case that mediation is not an option.
As a side note, in insurance cases in Texas, the jury is not allowed to know that any insurance money has been paid. So in a situation where someone is hurt in an accident by another driver then sues for medical expenses, the jury is not told that the medical expenses (are often) already paid for by the carriers. They're also not told that, no matter how much money they award, if it falls under the civil caps on awards (in Texas) that the judge will automatically lower their award after they leave the court room.