It's misleading. Obama tried to maintain funding UNESCO:

"In 2011, the United States stopped funding Unesco because of what was then a forgotten, 15-year-old amendment mandating a complete cutoff of American financing to any United Nations agency that accepts Palestine as a full member. Various efforts by President Barack Obama to overturn the legal restriction narrowly failed in Congress, and the United States lost its vote at the organization after two years of nonpayment, in 2013."

https://web.archive.org/web/20220503183152/https://www.nytim...