In some cases, as it might be in this one, answering the question without actually “touching” the problem and digging around the possibilities… may not be possible. As you already know from my article (stains on walls), there are several conditions that might be responsible for those dark stains.
If this house is only 16 years old, the furnace (if it is forced air) should not be an issue but I’ve seen some of them 15 years old, with cracked heat exchanger causing wall / ceiling stains and dumping soot onto the carpeting (you’d need a professional to check all of the fuel burning appliances, preferably nobody associated with the Realtor). If you’re positive that those dark stains have appeared (or their amount increased) everywhere after the hurricane, the chances are that they are mold related. There might be flooded crawlspace underneath the house (or just wet), high water table around and under the house that increases moisture level and causes mold growth, leaking wall finish, etc.
So, since the general home inspection is only a “visual” procedure (according to standards of practice, the inspector has no obligation to lift the siding to check for water damage, attempt to check wall interior for insulation, mold, etc., enter the attic if he feels that it might not be safe or could cause some damage, and so forth. He can but he is not obligated to do it. So, you need an experienced home inspector that is working for you / not for the agent, and will find the reason for those stains / not just state that there are stains.
It’s your money and I wouldn’t worry about the agent. I lost many of them while doing home inspections because they thought I should be obligated to perform inspection in such way that it guarantees successful deal. I can call you but I’m not sure if I’ll be able to tell you much more from Illinois. You just need a pair of experienced eyes.
Let me know,