From the article you quoted:
“ ‘This is truly remarkable,” Camarota and Ziegler write, “because natives accounted for two-thirds of overall population growth among the working-age population.” As a result, the number of US-born natives who don’t have jobs — both the unemployed as well as those who have dropped out of the labor force altogether — has swelled by 17 million since 2000. The takeaway? Far more native-born Americans would be working if immigrants hadn’t soaked up all the job growth since the turn of the 21st century.’”
The article disputes that conclusion with the simplistic, unsupported bromide:
“In the zero-sum world of the anti-immigrant advocates, foreign-born workers can only gain at the expense of the native-born. But in the real world, immigration generally enlarges the economy, boosts productivity, and adds jobs.”
They don’t analyze productivity figures at all, and they don’t determine how much economic growth is split between immigrants and native-born Americans. Economic growth doesn’t help Americans if all the growth goes to immigrants.
So your reference isn’t even close to proving the case that you use it for.
No, immigration suppresses wages for Americans. Supply and demand. It imposes costs on Americans.