On its face, it doesn't seem that crazy. Location is linked to both wealth and environment, which are both pretty significant factors in health. Do you think most doctors would say that average genetic variation makes a bigger difference than, say, poor childhood nutrition, or smoking?
I have no idea if that is true, but that is one way of reading the title without disregarding all the work done with genetics.
So if you have a classifier like ZIP, that (1) epidemiologists have done a bit of legwork correlating to classical markers like obesity (or their correlates, such as income and dietary/smoking/prescription patterns) and (2) tends to follow familial/ethnicity clusters in (3) a heterogeneous population, you can amass a fair bit of predictive power on the cheap for complex disorders where environmental variance plays a role, as well as beating the spread on behaviourally-determined mortality/morbidity factors.
It is likely that the predictive power of GRS-based approaches will improve for many conditions in the future (they are of course already powerful for Mendelian disorders).
I do have some doubts that the zip code actually gives BETTER prediction than the genetic risk score. I have difficulty believing that if someone had done a genetic profile on a patient and was willing to tell me either the patient's zip code OR the genetic risk score, that I would be better off asking for the zip code because it had greater predictive value. It' certainly not impossible (because of environmental factors that correlate with zip code), but it is surprising and I haven't yet seen actual research supporting it.
As someone who doesn't really care either way, I will say that his arguments have been more convincing than you simply casting doubt and demanding proof based on what seems to be a gut feeling.
To prove this sort of claim, you'd need to challenge the millions of hours of research geneticists have done, all the open data they've published, all the medical advances they've fueled. Instead, without even considering that the claim might be wrong, without any scientific humility, without linking to any supporting research, Harvard confidently makes the most extreme claim; that zip codes have more predictive power than genes!
Disgraceful and absurd that Harvard would publish something like this. Disgraceful that I believed it even for a moment.