That information has been written in various news outlets, including pretty reputable ones (such as BBC or Guardian), so I would assume it (mostly) true.
Diana's will (which is public) stipulated that her estate (including stocks, cash, jewellery and other assets) should be held in trust to be shared equally between her two sons. The original age when the brothers were to gain full access was 25, but it was later changed to 30 (although they did have access to income from interest on the capital since they reached their 25th birthdays).
One of the more interesting provisions of the will was that the brothers could change the shares each were to get, allowing Prince Harry to eventually get the lion's share, since William is guaranteed to one day have a huge income from the Duchy of Cornwall.
Some of Diana's jewellery was, strictly speaking, not hears but loan from the Queen; they returned to the Crown. Most of her jewellery is kept in trust, some may have even been sold. After her death, William and Harry were allowed to choose keepsakes from her collection; Harry chose the ring, while William - her Cartier watch (again, according to reports). The brothers, however, agreed (presumably, later) that the engagement ring will belong to the one who gets engaged first.