Can I be sued by someone else’s insurance company for their negligence?

There are two different answer to your question:
1) First, even if you are correct and you are not liable at all (see #2 below for more on that), the court doesn't know that when the lawsuit is filed; courts do not "prescreen" lawsuits to see if they are valid or viable. So even a lawsuit that will lose later can be filed in the first place, forcing you to respond to. (In that regard, note that if you fail to respond--for example, to file an "answer" within the appropriate time frame--then no matter how bad their suit, you will still lose by "default," which is like forfeiting a ballgame by not showing up for it.)
2) The other driver *may* have been negligent, if when they drove in, your grill was clearly visible and so they should have seen and avoided it. But if it was getting dark or was full dark out and your grill was small and/or dark-colored (like, for example, many of the smaller Weber kettle grills or the common small black rectangular grill with no legs or low legs), it might have been difficult to see under the circumstances and so they may not have been negligent or carless in parking by or over the grill. They were only negligent if the grill were visible enough under the circumstances that they should have seen it.
Also, regardless of their negligence, *you* were negligent: it is carelss to leave a lit or smoldering or hot grill unattended where there are other people, since one or another type of accident is not unlikely. (For example: a child in the parking lot could easily have fallen into or on it.) Your state follows "comparative negligence": if both sides are careless, the plaintiff can still successfully sue if he was not more negligent than the defendant (person being sued). As stated, there is essentially no doubt but that if you left a hot or smoldering grill unattended, that you were negligent. Even if a court were to conclude that the other side was negligent, too, if they were not more negligent than you, they could win money--which means that if a court thought you and they were equally negligent, they could get compensation. The amount of compensation would be reduced by their percentage of fault (e.g. if equally negligent with you, so that negligence is 50-50, they'd only get half the money they are seeking), but again, if they are not viewed as more careless than you, they'd get something.