I'm not wrong. I live in the US, and for various reasons that I'm not going to go into here, I am very aware of how scholarships and financial aid work for both domestic and international students.
Tuition is not the same as "cost of attendance".
A student looking to go to Iowa on international student merit scholarships plus a patchwork of other scholarships (faculty merit, special interest, specific population/ heritage, etc) would be trying to 'enter by the eye of the needle' - and there would be no real reason to do so when there are better universities in the US and elsewhere.
The bottom line is that an international student at Iowa would have to come up with $50k-$54k every year. This number is the cost of attendance, which is comprised of tuition, plus room and board, plus required incidentals such as various fees and student health insurance. As you can see, cost of attendance is significantly higher than tuition alone.
Depending on cobbling together several scholarships wouldn't be a good idea unless the student was either very gifted academically or very reckless, or had the bank of mom and dad to fall back on if the scholarships went to someone else. If they came up short for whatever reason, the bursar would politely explain to them that without their check for the full amount owed per semester, enrollment wouldn't be possible.
If very brilliant, why not try to get into one of the half dozen or so universities that offer a full ride to the highly qualified international applicants they welcome, if family finances mean they otherwise wouldn't be able to attend? MIT, Harvard, Princeton...