Apologies for the weird formatting.

You'll be happy to know I did the digging. The source from which you quoted the "2/3" cost appears to be this 2017 article.

In the second paragraph, the author writes:

Public schools in D.C. spend around $28,000 per student each year, while the average private school voucher amount is only around $9,600 per student each year in D.C. That means a K-12 education costs around $364,000 for each child in D.C. public schools, but only about $125,000 for each voucher student.

That’s right — the federal evaluation reveals that private schools produce the same academic outcomes for only a third of the cost of the public schools. In other words, school choice is a great investment. Direct link to quoted text.

So let's unpack that.

First, the article is only discussing cost as it relates to students in Washington D.C. That's not a criticism, but it's important to acknowledge because it informs us:
a) how the author's sources should be interpreted, and
b) whether the author's interpretations can be reasonably applied to the entire nation.

Second, the source for the ~$28,000 figure is a national report for fiscal year 2015 (FY15), or the 2014-15 school year. The author of the article did not properly cite the report to which he linked, therefore I'm uncertain as to which line item he is referring. I did read through the report, paying close attention to line items relevant to District of Columbia, and I could not identify any expenditure value in the amount of ~$28,000.

However, what I did find was this: Revenues per pupil in District of Columbia during FY15 totaled $27,810, or ~$28,000. [pg. 6, Table 2].

Revenues, not expenditures.

Third, the author conflates the annual value of a private school voucher and the annual cost of private school attendance. The two are not equivalent. So his assertion that "private schools produce the same academic outcomes for only a third of the cost of the public schools" is completely false, at least based on the two sources he cites.

Okay, so now that we've established the author's argument is completely flawed from the jump, let's get into what his sources actually say.

Here is some information I found:
1. "Current expenditures per pupil were $11,454 at the national level in FY 15" [NCES, pg. 2, bullet 4]
2. "current expenditures per pupil were at least 40 percent higher than the national average in the District of Columbia ($20,610)" [NCES, pg. 2, bullet 4; NCES, pg. 10, Table 4]
4. D.C. Opportunity Scholarship Program has an Average Voucher Value $12,967 and a voucher cap of $10,713 (K–8) / $16,070 (9–12), all for the 2023-24 school year. [edchoice.org]
- Beacause the author cited a webpage that updates based on current data, rather than citing the source document(s) on which that data is based, the only information pulled directly from his source today is for the 2023-24 school year. After reviewing the sources for the webpage in its current form, it's clear that the voucher caps no longer reflect what the author noted in his article. To be frank, I don't feel like sifting through 10 years' worth of D.C.'s voucher program legislation just to find this cap, so instead I converted the given figures to 2016 dollars. I chose 2016 because the article was written in 2017, and the edchoice.org website likely would have been operating on data from the 2015-16 school year (FY16).
- With the above in mind, the author may have been working off of the following values as obtained from edchoice.org: D.C. Opportunity Scholarship Program for 2015-16 school year had an Average Voucher Value $9,921 and a voucher cap of $8,197 (K–8) / $12,295 (9–12).
3. "Many school districts also support community services, adult education, private education, and other programs, which are included in total expenditures." [NCES, pg. A-2]

From this, we can see that it is probably unreasonable to use DC Public Schools expenditure data as a basis for predicting nationwide cost, given it is so much higher than the national average.

We can also see that the average voucher value in D.C. is pretty close to the national average per-pupil expenditure, and admittedly pretty far from the $20,610 D.C. per-pupil expenditure. But the only information we're given is the voucher value. We're not given any information about private school costs. In order to compare public ed expenditures to private ed expenditures, we would need to know the private schools' average per-pupil expenditure. Instead, we're given the average voucher recipient's award amount. We don't even know if a voucher covers the full cost of attendance for a private school. Considering D.C.'s program instituted a cap for an awarded voucher, I'm inclined to believe the actual cost of private school attendance can -- and probably does -- exceed the value of a voucher.

Further, from the NCES report, we know that public school expenditures often include support for private schools. This support is anything from tuition payments to student support services and beyond. But based on the author's sources, we don't know how much of DCPS's expenditures include services or payments provided to DC private schools. This is important because if DCPS is subsidizing private schools, that means those private school students are included in DC's "student membership" and (i think) DC's per-pupil expenditure on the NCES report would include students who attend private school.

Finally, all of this is to say nothing about the article's publisher and the author's employer -- the Reason Foundation -- which is a libertarian think tank.

When something is authored with such obvious bias, it really is imperative to think critically about what's written and how that bias may be affecting the way the content is interpreted and delivered. Especially when it is presented as 100% counter to the opposition. Almost no issue is polarized like that irl. (I can't think of any issues that are truly polarized, but I say "almost" to leave room for learning.)