I've seen that article floating around more than once, and it stinks as much now as it did in 2000. Don't believe everything you read on the Internet. It irritates me because there is enough real and factual controversy, disagreement and issues surrounding the creation of park areas without having to embellish things. I call BS on the "no compensation" claim.
Having lived in the area for five years earlier this decade I have a little knowledge and interest of the history of the area in the post-WW2 period.
First of all, Mo Udall was never Sec. of the Interior, Stewart Udall was. Mo Udall was a Congressman. Stewart Udall was SecInt from '61 to '69. He visited the Canyonlands first in 1960 while looking into the Glen Canyon and Rainbow Bridge issue downstream, meeting with legendary Floyd Dominy, head of the Bureau of Reclamation. On the way to Denver afterwards in Dominy's plane he flew over the area and was intrigued. Later he visited the area again with Utah and Congress officials and toured the area by helicopter. In July of 1961. There is no record of him ever having met the Tangrens (though it certainly isn't out of the realm of possibility.) The trip in 1970 is flat out wrong. Nixon never had anything to do with it. By his term the park had already been created (1964) and Udall was no longer SecInt. Makes you wonder about the rest of Swint's assertions in the article. Maybe he should stick with aviation subjects or his religious writings.
Being curious, I emailed a friend who works in cultural resources preservation and history in that region of the NPS. Most parks have an administrative history that you can tap into, unfortunately the one for Canyonlands doesn't appear to be online. If anyone cares I'd be happy to forward what I found out about the Tangren's compensation for their previous holdings.
What is certain is that Tangri-la is a cool place to visit, and that Bud Tangren has been, and presumably still is an interesting character.