This just shows that IQ tests are garbage. Top level math contests are a much better indicator of your intelligence. I don't know what tests you're talking about because USAMO and Putnam don't have internationals.
And what mathematicians are you talking about? Take time to look them up because I can think of no examples of great mathematicians being "bad at proofs". That would mean they were bad at logic, which would mean they were bad at math. Being more famous for a conjecture doesn't mean you were bad at proofs. To even produce those conjecture requires deep understanding of the math leading to it. I can almost guarantee that there are no great mathematicians who would zero Putnam. I don't even zero Putnam, and there are plenty of people way better than me who still have no chance of becoming a great mathematician.
Do you realize how brilliant a mathematician has to be for you to even ever know his name?
International students can take Putnam if they go to school in the US, no? I could be wrong on this.
And what mathematicians are you talking about? I retract that: "sucked at proofs" is too strong a statement. There was a time when the same degree of rigor wasn't expected, so a lot of great mathematicians never or rarely wrote proofs. An example would be Ramanujan, who contributed immensely to mathematics and had amazing intuition, but who rarely wrote proofs and, when he did, Hardy usually had to fill in the holes.
On the other hand, had Ramanujan desired or needed to learn how to write rigorous proofs, there's no doubt that he would have been able to do so.
As for Putnam as a "better indicator" of intelligence than IQ tests, I'd agree, but it still only measures one kind of intelligence. The problem with IQ tests is that they aren't accurate in the upper ranges (140+) because that's not what they're designed for.
First of all, you can study for those (although virtually all of us hit a ceiling because those problems are very hard). I used to study for those tests (although technically not IMO since I never qualified for it) and did reasonably well, although my IQ is "only" about 150. If these tests were perfect IQ tests, I shouldn't have even placed in the top thousand... since there are 400-4000 Americans smarter than me per year, plus the international students. (However, my "math IQ" if such a thing could be measured would probably be around 165-170, and "verbal IQ" around 135-140.)
Also, there are a couple of famous mathematicians (names don't come to mind) who are notorious for sucking at proofs. Their conjectures were very good and almost always right, but they relied on future mathematicians to prove their work (details, details). They would likely zero the Putnam.
