I think there's a fundamental problem in how to interpret this analysis. It says that a company is founded by an immigrant if there is at least one immigrant founder. This means that if 1 of 10 founders is foreign born, then it classified as immigrant founded. An aggregate calculation like this is very likely to give a number which is higher than the more important number, the over- or under- representation of immigrant founders relative to the immigrant population.
For example, if every company has 10 founders, and every company has 1 immigrant founder, then by the given definition, 100% of the companies would be founded by an immigrant. However, only 10% of the founder population would be an immigrant. As immigrants make up about 13% of the US population, this would mean that immigrants would be proportionally less likely to be founders of $1B valuated startups than non-immigrants.
Curiously, and I believe significantly, the study does not give this population information, and it makes it difficult to determine that ratio.
I did not find an explicit count of the number of immigrant founders. Table 4 has a list of all of the name, and Table 3 has a count of immigrants from a given country, so it's possible to figure this out. I am perturbed that the first contains 60 people and the second 61. Perhaps I have miscounted, but I believe there is an error in the report. (I double checked the report by searching for "60" or "61", but found no explicit total of the number of immigrant founders.)
I did not find an explicit count of the total number of founders, which means I have to compute that myself from the list of companies. I did not find an explicit list of companies, which means I have to go to the original WSJ data source.
Which I did, though my count was off by one from the report's count. It would have been much better if the report included the explicit list of companies and founder counts.
I took the current WSJ list of 106 companies and picked a few in the top, middle, and bottom range. (Statistical sampling would have been better, I know.) I found founder counts of 65 of them before tedium kicked in. I found 161 founders.
This gives an estimated total founder size of 161/65x87 = 215.5, and implies that about 60/215.5 = 28% of founders are immigrants.
This number, while twice as large as expected from the general immigrant population of the US, is also around half of the eye-catching 51%.
The next step would be to do a sensitivity analysis to give an idea of error bars. I do not know anything beyond basic statistics, but will point out that 60 is a very small number compared to the number of foreign visa, and hardly representative.
Speaking of statistics, while 28% is twice as large as 13%, there's likely also a form of p-hacking, or "garden of forking paths" going on. With enough sampling, you will be able to find very unrepresentative subgroups in your data. Why was this population of $1B startups chosen? Do the results change with $2B? Do they change for companies that go public?
For a more specific example, last year there was an analysis going around which pointed out that "Most high tech companies are founded by founded by First/2nd gen immigrants". This is definitely in the same vein, though with different measures. See https://news.ycombinator.com/item?id=9085970 for my observation that this is almost exactly what you would expect given the immigrant population in the US.
Since I can point to two reports related to the topic, how many more negative and thus unpublished correlations are there?
Finally, the report includes the suggestion that diversity among the founders helps improve the success of the company. If that were the case, then should we not exclude companies where the all founders are from the same foreign country, as in Nutanix where all three founders are from India?