The evidence for asthmatic patients not being at increased risk comes from this paper: onlinelibrary.wiley.com/doi/pdf/10.1111/all.14238 which compared the characteristics of patients with mild and severe disease. This concluded that asthmatics and those with COPD were not more severely affected.
However, it's worth bearing in mind that a relatively small number of patients were studied and actually there were no asthmatics in the study groups. I'm not convinced that this is a basis for saying that asthmatics are not at risk. The paper also had a very low number of smokers (9 out of 140) yet we know that rates of smoking are very high in China. This would suggest to me that either smokers and those with respiratory diseases are less likely to develop covid-19 or, more likely, the group of patients they looked at was not representative. Especially considering a much larger study did show an increased risk for chronic respiratory disease.
Having said that, chronic resp disease is a broad umbrella, and there is likely to be a big difference between say, a current smoker with COPD on oxygen therapy and someone with mild, well-controlled asthma.