‘Vibhu’ means, The Almighty,Bhagavan and ‘Uti’ means Protection.
So Vibhuti means the protection of Bhagavan.Therefore When God gives the scared ash to someone, it means that (ash) is for the (special) protection of the person. Similarly it is the same protection when HE gives some other material objects to some other people. So if we did not get these from HIM , it means HIS protection is there for you and you do not need any special protection.
Courtesy; Brahmin association