This is the first time I heard of it. I eat rice about three times a day (it's our staple food) and I have asthma ever since I was a kid but I hadn't had any problem with it. Not with rice thou, but on what comes along with it or what I eat along with it. When I have asthma I eat rice with boiled eggs, noodles or whatever my body tend to want as I am sensitive on meat and other foods. But no, not with rice.
But one thing also, since you mentioned asthma and chronic cough, cold drink is another thing my body doesn't want me taking when I have either chronic cough and specially asthma. It makes my asthma attack worst.