The arya samaj does not consider the puranas to be a part of shruti. Hence the material in the puranas which do not conform to the vedas is false by default. Yajurveda 40/8 says AUM is AKAYAM; hence avatarvad [kalki avataar] is against vedas. Further this purana talks of quranic and biblical prophets. Since the vedas do not contain history; these materials are not the word of AUM. Again, the vedas give knowledge useful to humans i.e. how to lead life here and attain mukti. They do not indulge in prophecy.
Thus, whether Mohammed, the Prophet existed or not; did he write the quran or not; whether this purana or that hadith talks about him; we r least bothered. All we need to know is that he was not on the vedas and hence was not on the right path.