Pretty sure the base rate you'd want to compare against is either placebo given -> remission or simply spontaneous remission. It appears that spontaneous remission is really quite rare.

> [sponanteous remission of cancer] incidence is roughly one in every 60 000–100 000 cancer patients, but the true figure is unknown (2). Spontaneous regression of colon cancer seems to be particularly rare

https://academic.oup.com/jjco/article/45/1/111/888056

So using 0.0016% and 12 patients (which is what the paper the NYT actually links)

For a ~50% chance of seeing one trial with 12 patients have complete remission you'd expect to see ~43k trails.

(1 - 0.000016)^43000 = 0.502577

I wouldn't discount this study based off of those numbers.