Their statement for "third party payment" is industry jargon for "don't ban it," because Americans equate "uninsured service" with "unavailable service." Outside the headline, their strongest position is "don't make it unavailable."
And what argument do they make for it?
They trawled the data for things like reducing the transmission of HIV - which it does, in third-world country where condom usage is low, antiretroviral usage is low, pre-exposure prophylaxis is low. In first-world countries, circumcisions have not been shown to be protective, because in a setting with a higher baseline level of antiretroviral and condom usage, its effect is somewhere between negligible and non-existent.
The AAP is writing recommendations for America, not the third world.
Likewise, the reduction in cancers is a tiny effect. Small to begin with and, again, negligible in first-world countries.
As other pediatric bodies outside the AAP noted, including these "benefits" is a reach, and the AAP got raked over the coals for doing so.
So, no, not literally - the AAP made a strong political soundbite headline, and then walked it back in the text of their position paper, because they couldn't defend that headline.
And certainly not unambiguously, when they were widely criticized for relying on weak studies that didn't apply to the population in question.
The AAP isn't a terrible organization, but it's not immune to politics, and this shift in their official stance was political, not data-driven.