Quite so, although I'm sure Robert was speaking more generally when he said "inherited".
Purchased by Prince Albert from the Gordon family (owners of the Abergeldie estate), Birkhall remains part of the larger Balmoral Estate. According to its own website, the estate comprises 18,659 hectares owned between Balmoral, Birkhall and Glen Doll, 2,940 hectares of grouse moor at Corgarff and 4,688 hectares of sporting rights rented from a neighbour. 3,000 Hectares are afforested and 222 hectares are arable or pasture, with 100 Highland Cattle, and The Queen's Highland, Fell and Haflinger ponies.