Not sure if this is the study that proves it - since due to ethical considerations it's simply observational, and doesn't control for confounders and introduces a lot of bias - but, it's a small piece of the puzzle.
This is a cohort in a Montreal pediatric emergency department in which they prospectively collected data on moderate and severe asthma exacerbations as patients progressed through their care pathway. They see, essentially, a nonsignificant trend in increased odds of hospital admission for patients in whom administration of systemic steroids was delayed. This is mostly a data mining exercise, so any significant associations should be considered hypothesis generating. However, considering the patients who received delayed steroids had milder exacerbations overall - yet still seemed to go on to have higher admission rates - it might be tempting to interpret these findings as appropriately confirmatory of physiologic foundations of treatment.
At least, there's no suggestion of harm from early steroid administration in asthma with exacerbation in children. Perhaps some prospective interventional data with patient-oriented outcomes will surface in response.
"Early Administration of Systemic Corticosteroids Reduces Hospital Admission Rates for Children With Moderate and Severe Asthma Exacerbation"