Theoretically, one should be judged based on publications, and not where they obtained their PhD. But the ugly truth is obtaining a PhD in the US give you more advantage when applying for a academic position in the US. This is an advice that I heard several times, by different people to different people.
Last year, there was a young researcher interviewed for an Assistant Professor at my university. I looked up his profile, and was totally impressed. At that time he were just 3 years after PhD, but he had published nearly 40 papers, and most of them are in the big 4 conferences in my fields. He also got more than 2000 citations (more than 3000 now).
His working experience includes research positions at the likes of Google, Facebook and he were postdoc at a top 3 university at that time.
However, at the staff lunch when he joined as part of the interview. A staff, director of some sorts (student career or whatever), introduced him to everybody, summarized his bio like "he did his undergraduate at Stanford, then he went to the UK where obtaining a PhD is much easier hahaha". I didn't know how he felt, but I felt being insulted myself. I also got my PhD from the UK, although at a much lesser school, not Oxbridge like that guy.
I don't know why he didn't get the job, he is still a postdoc at the same university. The one who got the job is a lady from a Ivy League school. She is also very talented, but her publication record and experience was nowhere near his, she even hadn't graduated at that time.