The difference between L1 and L2 language competency is deeper than whether you acquired multiple languages in "parallel" or "serially". The competency level, whether you are fluent or near-fluent, is based on the critical-learning period which ends roughly at the onset of puberty. Nothing rules out acquiring multiple L1s in serial, which I suspect to be the case in many instances of multilingual children.

Moreover, the author's anecdotal support is in contradiction with the fact that children do acquire multiple languages largely without problem. There are effects of one language on the other, but they are different in natural, and far less frequent, to crossover effects in L2 language learning, e.g. learning Spanish is high school.