How are international graduate applicants perceived by universities in the US?
To answer your specific questions, schools are generally trying to admit the best applicants (who will choose to come), not just a group of people of the right size over a certain threshold.  So if an international student appears to be a stronger candidate (evaluated the same way any other applicant would be), the international applicant is likely to be preferred.

Graduate students are generally funded based on packages that don't take into account where the student's from, so it's not generally more expensive.  (International students may be less likely to accept because the funding is less likely to enough, but that's no reason not to admit them.)

Finally, why would international applicants be any less trustworthy or appropriate than domestic ones?