This seems like a scheme that will be ripe for gaming / outright fraud. How exactly does the U.S. verify anything? Basically the only way to do this would be to have control over some kind of verification system that comes from vetted and registered hospitals.
Even then you have so many problems. There is no realistic way to even partially guarantee that forgeries won't happen regardless of your vetting system. And add to that the fact that the U.S. government has no control over regulations in foreign countries, so there is no way to force validators into compliance.
A half-baked plan that will screen out only some COVID carriers is better than the status quo where we screen out none of the COVID carriers.
In Hawaii, they have limited partnerships and Hawaii verifies the result directly with the labs. It says on the website they'll prosecute anybody that submits forgeries, but it's true that this is much easier to do when everything is within the same country.
My experience flying from the US to France through Portugal was that an agent at the gate looks over whatever paper you give them and highlights "PCR", "NEGATIVE" and the date and then hands it back.
Then in Portugal they asked for the paper and waved me through, and the same at the French border.
So logistically, pretty easy to fake (unless you're stupid enough to be trying to buy the fakes in the airport like some guys who got caught in Paris a few months ago) but I agree with other commenters it's better than nothing and will almost surely improve the rates of testing/precaution around travel.
When I got the PCR COVID test administered when I had a suspected case, I was required to fill out a form stating my name, DOB, email, phone, physical address, full social security number, and student ID (I'm a college student). Since these are all attributes bound to identity, I'm sure it's not too difficult to make a database of test results.
...Just from the thought of it, forcing other countries to store your private info would be a terrible idea considering they probably could care less about it being stolen.
But, you are entirely missing the point. The U.S. cannot mandate that other countries maintain a database with U.S. citizens personal info, even if your idea didn't have massive gaping holes in it regarding security. It is simply impossible.
Forgeries of the international yellow fever vaccine certificate happen regularly. (For example, backpackers to Africa from Eastern European countries where the yellow fever vaccine was perennially unavailable at our local clinics printed out their own copy on yellow paper and put a fake stamp on it.) Nevertheless, the yellow-fever certificate requirement is believed to work well enough regardless. With COVID, too, one could argue that something is better than nothing.
I mean the number of people who are willing to commit forgery and lie to border patrol is probably pretty small. This is a huge step in the right direction that will prevent loads of air transmission. We don't really have time to wait years for a "fully baked" solution, and this is a solid compromise.
It doesn't need any of that to be nearly entirely effective. The vast majority of people traveling into the country are not going to attempt to falsify documents.
Even then you have so many problems. There is no realistic way to even partially guarantee that forgeries won't happen regardless of your vetting system. And add to that the fact that the U.S. government has no control over regulations in foreign countries, so there is no way to force validators into compliance.
This sounds half baked to me.