Rumsfeld's assertion seems reasonably accurate.

https://dailycaller.com/2021/08/21/biden-circa-1975-argued-against-evacuating-vietnamese-refugees/

When the North Vietnamese marched on Saigon in 1975, thousands of South Vietnamese citizens — many of whom had connections to the U.S. — asked for assistance in leaving the country. [...] Then President Gerald Ford called on Congress to authorize funds to evacuate 2,500 American citizens and their families along with about 175,000 refugees — and Democratic Delaware Sen. Joe Biden was one of the loudest voices in opposition, according to The Atlantic. In an April 14, 1975, meeting between the president and the Senate Foreign Relations Committee, Biden said, “I feel put upon in being presented an all-or-nothing number. I will vote for any amount for getting the Americans out. I don’t want it mixed with getting the Vietnamese out.” Ford pushed back, arguing that “our tradition is to welcome the oppressed.”

“I do not believe the United States has an obligation, moral or otherwise, to evacuate foreign nationals,” a young Sen. Joe Biden said in 1975.

Biden repeated his position in remarks a week later. “The United States has no obligation to evacuate one, or 100,001, South Vietnamese.”

I believe the Vietnamese that Ford (and others) most wanted to rescue were anti-communist, pro-American collaborators.

More: https://redstate.com/nick-arama/2021/08/17/youll-never-guess-who-was-also-involved-in-the-1975-debacle-in-saigon-n428530