In a way, it's similar in nature to how people will, with best intentions, tell you to smile more if you have depression.
I think the issue is many people don't understand the problem and they can't see it. In fact, someone with a common cold can expect to get more sympathy and better advice than someone with a chronic illness. The second issue is that many people struggle to think of something to say, its quite uncomfortable and the automatic choice is to give advice.
Interestingly for people with colds the sympathy is also commonly misplaced, at least mistimed, namely the outer symptoms often only show up after the worst parts (sore throat, dizziness, nausea, headaches) are already overcome.
Almost like the old saying "out of sight, out of mind".
Personally, I was going through some rough stress at work. Minute someone comes down with a cold, they got "oh god you don't look well at all. Have you spoke to the boss?". 5 minutes later I would get "so why isn't x done yet?" by the same person despite it being a known fact I'd been holding the weight of a two man team on my own for 18 months!
That made me feel even worse but once I got a handle on things (and an extra pair of hands), I noticed the interesting pattern in general.
I think the issue is many people don't understand the problem and they can't see it. In fact, someone with a common cold can expect to get more sympathy and better advice than someone with a chronic illness. The second issue is that many people struggle to think of something to say, its quite uncomfortable and the automatic choice is to give advice.