The complaint is that these delimiters are really only meaningful for Western Europe - the delimiting events both happen in Italy. One of the running themes of early medieval Arab history is, after all, wars with the (eastern) Roman empire. So it's a bit like talking about Elizabethan Turkey, or Warring States-era Brazil.
The fall of the Roman Empire basically allowed the Islamic Empire to exist. Even if Muhammad had arisen while the Roman Empire still existed he would have been limited to the greater part of the Arabic peninsula.