First of all, its not a rumor. Its a fact, described in the 3rd Edition of the Pocket Guide to the Empire.
The political weakness of Valenwood has been evident for more than twenty years now, and the Bosmer seem resigned to this state of affairs. The land is considered by most to be a mere geographical designation without any political purpose. If there is honor or pride, it is with one's family or clan. National feeling, never strong, seems to have died. The tribal council has not met in decades. Valenwood appears to be adrift.
And yet there are signs of other forces stirring. The Wild Hunt has been sighted for the first time in over five hundred years, although to what purpose is not yet clear. Falinesti, the “walking city” of trees, has rooted itself for the first time in recorded history. A new Bosmer prophet has arisen, known only as the Precursor, who preaches that the old Forest God Y'ffre is returning with new gifts for his favored people. Whether these are isolated events, or signs of some great change coming to Valenwood, remains to be seen.
The "current events" that the book relates took place a year or more before Oblivion. And Falinesti is described as simply "rooting itself", albeit for the first time in recorded history. The idea that Falinesti is indeed Green-Sap is circumstantial at best, but even if we assume that it is, the fact that it rooted itself doesn't make it probable that it was deactivated. It is certainly an important gesture (perhaps it was preparing for the coming Oblivion Crisis), but we haven't heard high nor hell from it since, some 200 years later. For all we know, it uprooted itself and continues on its merry migration. The fact that Skyrim loading screens give some mention to migrating trees should be enough to calm anyone's fear that it is deactivated.
I don't think White Gold is deactivated either. In Lord of Souls, it seems perfectly functional. It is likely that its not broken, but rather it is no longer serving its former purpose.