Yes, I make that distinction. And it probably is ok going by the Data that I have of international applicants to US schools and European schools (Insead and LBS only). This is only my perception and small sample data, please do not take it as gospel truth. Maybe my bias, since I am an international applicant.
The reasons why a higher GMAT is often a plus for an international applicant are two :
A) Almost all other information is slightly ambiguous for most of the faculty members. If 10 people say they are a 3.7 GPA from XYZ University in China, what does it mean ? And what if you are a 3.7 from Princeton? It obviously depends on whether XYZ has a good record/prestige etc. But given a choice, a PhD program committee (say of a US School) will have an easier time
deciding whether that Princeton graduate is PhD material than that applicant from China. And therefore these faculty members (maybe subconsciously) favour using GMAT as a critical differentiator.
B) The international applicant pool is large. And competitive. A higher GMAT signals a better preparation for the program
Net, for shortlisting within an international pool, GMAT is a quick, reliable shortcut. For shortlisting within an American pool, you are not so sure of GMAT as a differentiator. Beyond the shortlisting, other things matter.
Is this true ? MAYBE.
Can you take a chance? Maybe at 720. Maybe not at 680.
IS GMAT CRITICAL THEN ? NO - GMAT, SOP, GPA, EXPERIENCE, INTEREST, EVERYTHING matters. The application package is a whole. But you can improve on GMAT and SOP, not your GPA and experience (at least not in the last two months of application
.) So, there - Good SOP and Good GMAT => Increased admit chance for internationals!