Certainly PhDs from non-obscure schools are accepted by US job market. E.g. my maths PhD is from University of Western Australia, and in few job applications I did in US it was never an issue.

It's a bit more hassle at the time you actually need to get an H1-B visa, then your non-US PhD needs an extra certification, called "credential evaluation", done by a member of a member of the National Association of Credential Evaluation Services (at least it was the case for me). They take your electronic degree transcript (which normally available in Australia), charge you something like US$200, and provide "credential evaluation report" for the prospective employer.

Certainly PhDs from non-obscure schools are accepted by US job market. E.g. my maths PhD is from University of Western Australia, and in few job applications I did in US it was never an issue.

It's a bit more hassle at the time you actually need to get an H1-B visa, then your non-US PhD needs an extra certification, called "credential evaluation", done by a member of the National Association of Credential Evaluation Services (at least it was the case for me). They take your electronic degree transcript (which normally available in Australia), charge you something like US$200, and provide "credential evaluation report" for the prospective employer.