it has a checklist to answer your question.
I am not so sure it is either/or. Probably your product/business people are as concerned about the success of your product as you are, so if you bring up this issue that communication is a problem, maybe they'll be responsive.
Working across time zones require some adaptation. Often I have meetings at 8am in the morning with people in Europe and Asia, sometimes I have meetings at 8pm at night. If you have a few people who do liasoning on each side, they could each shift schedules by 1 hour and then you have a three hour overlap. You can get better at written communications, there really are a lot of options.
Definitely when you can't get in the face of a "product manager" there are some people who really won't do the job, and sometimes they won't if you can get in their face.