Ellen White mentions "as a matter of fact" that people of her day could not explain the remains of humans that were being found - much larger than people today. It is not so surprising that she would claim that such remains would be expected given the details about the pre-flood world -- but it was very surprising that she claimed people were digging up something along those lines.
Then in connection with the story in the OP here - I found this for the claims that were being made in her day -
Aside from mythology and folklore (see Tall tales), remains of extremely tall people have been reported, and documented in the Americas and other parts of the world. These are usually classified as remains that indicate persons of between 7 (2.15 m) and 12 feet (3.65 m) in stature.
The book Forbidden Land by Robert Lyman (1971) recounts the following alleged finds:
A decayed human skeleton claimed by eyewitnesses to measure around 3.28 meters (10 feet 9 inches tall), was unearthed by laborers while plowing a vineyard in November 1856 in East Wheeling, now in West Virginia.
A human skeleton measuring 3.6 meters (12 feet) tall was unearthed at Lompock Rancho, California, in 1833 by soldiers digging in a pit for a powder magazine. The specimen had a double row of teeth and was surrounded by numerous stone axes, carved shells and porphyry blocks with abstruse symbols associated with it.
Several mummified remains of humans with reddish hair claimed to range from 2-2.5 meters (6.5 feet to over 8 feet) tall were dug up at Lovelock Cave, (70 miles) north-east of Reno, Nevada, by a guano mining operation. These bones supposedly substantiated claims for legends by the local Paiute Indians regarding giants which they called Si-Te-Cah. However, there appear to be no verified Paiute legends about giants or that call the Si-Te-Cah giants . Some of these artifacts can also be found in the Nevada State Historical Society's museum at Reno. Adrienne Mayor states that these skeletons are normal sized. Mayor does not mention that some of the fiber woven sandals found at Lovelock Cave are extremely large, as great as 7 inches across the toes and over 15 inches in length (size 20 US mens) suggesting persons very much more than average size.
A 9' 11" (3.02 meters) skeleton was unearthed in 1928 by a farmer digging a pit to bury trash in Tensas Parish, Louisiana near Waterproof. In 1931 a 10' 2" (3.1 meters) skeleton was unearthed by a boy burying his dog in Nearby Madison Parish.
Aside from in Forbidden Land, we can find verified and unverified examples about the remains of giants:
The skull of a youth 7 feet tall, and the partial limb bones of a man estimated at over 11 feet tall were unearthed in 1890 at the Bronze age cemetery of Castelnau-le-Lez, France and published in the science journal "La Nature" and subsequently reported in the New York Times in 1892.
A 9' 8" (2.95 meters) skeleton was excavated from a mound near Brewersville, Indiana in 1879 (Indianapolis News, November 10, 1975).
In Clearwater, Minnesota, the skeletons of seven giants were found in mounds. These had receding foreheads and complete double dentition
A mound near Toledo, Ohio, held 20 skeletons, seated and facing east with jaws and teeth "twice as large as those of present day people", and beside each was a large bowl with "curiously wrought hieroglyphic figures." (Chicago Record, October 24, 1895; cited by Ron G. Dobbins, NEARA Journal, v13, fall 1978).
Near the city of Thunder Bay, Ontario there is a span of mountains five miles long that is in the shape of a man wearing a headdress lying down on his back. The span is called "The Sleeping Giant" from local Ojibway legend that identifies the giant as Nanabijou, the spirit of the Deep Sea Water, who was turned to stone when the secret location of a rich silver mine, now known as Silver Islet, was disclosed to white men. 
Patagons of Patagonia in South America, are giants claimed to have been seen by Ferdinand Magellan and his crew. Drake reported only finding people of 'mean stature' although his Chaplain reported giants. However, even before Magellan, a Spanish romance called Primaleσn of Greece was published in 1512 in which a dashing explorer discovers savages, one named Patagon, whose descriptions are very similar to those of Magellan.
There is even a story in William Cody's autobiography about an encounter with the Pawnee Indians that reads. "While we were in the sandhills, scouting the Niobrara country, the Pawnee Indians brought into camp some very large bones, one of which the surgeon of the expedition pronounced to be the thigh bone of a human being. The Indians said the bones were those of a race of people who long ago had lived in that country. They said these people were three times the size of a man of the present day...