It still would have been nice if they'd done a control group, an allergen-only group, and an allergen-and-probiotic group – all from the exact same initial rand

It still would have been nice if they'd done a control group, an allergen-only group, and an allergen-and-probiotic group – all from the exact same initial randomization and using the exact same administration/follow-through practices. That would have best quantified what, if any, added benefit the probiotic creates.