Correct, if your Carrier agrees that your defense is "solid" and willing to go to trial they will cover for whatever the outcome. The problem arises is if you believe your case is "solid" but the carrier can settle for $100K. The carrier will push hard to settle the case and may even threaten to not cover any of the losses beyond your policy limits.
The way the USA system works is even if you win at trial the case will cost the carrier $200K+ to defend. The Plaintiff doesn't pay a dime of these costs so the malpractice carrier eats it.
Blade - Be careful with this one. Certain medmal carriers and policies have the defense costs built within the liability limits; thus eroding one's liability limits. A policy needs to specifically state that legal defense costs are covered outside of the liability limits.