Is a Muslim considered an innovator (mubtadi') or disobedient (ʿāṣin) if he takes the initiative to greet an arriving person who has not offered the greeting? And should he offer the greeting again to the arriving person if the latter has not offered the greeting?

It is from the Sunnah that the one who is walking greets the one who is sitting, the one who is riding greets the one who is walking, the young greets the old, and the one entering greets the people of the place, due to the Almighty's saying: (So when you enter houses, greet yourselves with a greeting from Allah, blessed and good) [An-Nur/61], and the Prophet's (peace and blessings be upon him) saying: "The rider greets the one who is walking, and the one who is walking greets the one who is sitting, and the few greet the many." Initiating the greeting is a recommended Sunnah, and returning it is obligatory. If the one entering does not greet, but those in the house greet, or if the one walking does not greet, but the one sitting greets, there is no harm; rather, he would have done good and fulfilled the Sunnah of greeting, and it becomes obligatory for the other to return the greeting. If they act contrary, and the one walking greets the rider, or the one sitting greets both of them, it is not disliked; rather, it would be contrary to what is most preferable.